Infobox Single See Wikipedia WikiProject Songs Name Why Do You Have to Be So Hard to Love? Cover BAwdy.jpg Cover size Border Caption Artist Bryan Adams Album Room Service Bryan Adams album Room Service A side B side Released 2005 Format Recorded Genre Rock music Rock Length 2 58 Label Universal Music Group Universal Writer Bryan Adams, Gretchen Peters Producer Bryan Adams Audio sample? Certification Last single Room Service song Room Service br 2005 This single Why Do You Have to Be So Hard to Love? br 2005 Next single So Far So Good song So Far So Good br 2006 Misc Why Do You Have to Be So Hard to Love? is the fifth and last single by Canadian rock singer Bryan Adams , from his studio album Room Service Bryan Adams album Room Service , released in 2005 See 2005 in music . Even though the single proved a flop in the United States , it was successful on the Canadian AC chart. References reflist Bryan Adams singles Category 2005 singles Category Bryan Adams songs Category Songs written by Gretchen Peters Category Songs written by Bryan Adams pt This Side of Paradise ... more details
right upright thumb Facsimile of the title page of Measure for Measure from the First Folio , published in 1623 Measure for Measure is a play by William Shakespeare , believed to have been written ... 7 2 For in the same way you judge others, you will be judged, and with the measure you use, it will be measured to you. Date, text and authorship Measure for Measure is believed to have been written .... As a result and for a variety of reasons, some critics have labelled it as one of Shakespeare ... disguised as Friar Lodowick. Isabella , a novice nun. Claudio , Isabella s brother. Angelo Measure for Measure Angelo , rules in the Duke s absence. Escalus , a lord. Lucio , a debauched lord. Mariana ... end Synopsis Image William Hunt Claudio and Isabella Shakespeare Measure for Measure.jpg thumb right ... of a strict judge, Angelo Measure for Measure Angelo . Claudio, a young nobleman, is betrothed unofficially .... This did not make them unique however at the time most people including the Church would have considered ... have it, a pirate named Ragozine, of similar appearance to Claudio, has recently died of a fever ... Measure for Measure Angelo , which Angelo smoothly denies. As the scene develops, it appears that Friar ... in 1565. ref name Bawcutt N. W. Bawcutt ed. , Measure for Measure Oxford, 1991 , p. 17 ref Shakespeare ... or may not have been aware of. The original story is an unmitigated tragedy in that Isabella s counterpart ... of the text of Measure that survives today is not in its original form, but rather the product ... Press, 1993 . See also Shakespeare s Mediterranean Measure for Measure , in Shakespeare and the Mediterranean ... William Topham The earliest recorded performance of Measure for Measure took place on St. Stephen s night, 26 December 1604. During the English Restoration Restoration , Measure was one of many Shakespearean ..., appears not to have succeeded on stage. Charles Gildon returned to Shakespeare s text in a 1699 ..., Measure for Measure, New York, Penguin, 1998 pp. 181 183. ref Notable more recent productions ... more details
wiktionary measure tocright Measure may refer to Legal List of Church of England Measures Measure of the Church of England is a law passed by the General Synod and the UK Parliament equivalent of an Act Measure of the National Assembly for Wales , a law specific to Wales passed by the Welsh Assembly between 2007 and 2011 Measure of the Northern Ireland Assembly 1973 Mathematics and science Measure probability , a mathematical construct that models a real world experiment Measure mathematics , a way to assign non negative real numbers to subsets Measure physics , a way to integrate over all possible histories of a system in quantum field theory Units Measurement , the process of establishing the magnitude of some attribute of an object relative to some unit of measurement Bar music or measure, a unit of time in Western music representing a regular grouping of beats Coal measure is a seam of coal Measure termination , a way to describe termination of processes, algorithms, or functions Measure bartending or jigger, a bartending tool used to measure liquor Other Measure album , a 2000 album from Matt Pond PA Measure data warehouse , a property on which calculations can be made using precomputed aggregates Measure typography , in typography refers to the width of a block or column of text from the left margin to the right margin Countermeasure , a system designed to prevent weapons from acquiring and or destroying a target disambig cv de Ma es Medida fr Mesure it Misura he pt Medida hu M rt k ... more details
wiktionarypar hard hardness Hard or Hardness may refer to Hardness , resistance of physical materials to change under force Hard water , water with a high mineral content NP hard , a term used in Computational complexity theory Hard, Austria , a town in Austria Hard Z rich , a quarter in Z rich Hard tennis , a type of tennis court Hard music festival , concerts and live events Hard, or hard on, a slang term for an erection Hard nautical , a firm or paved beach or slope convenient for hauling vessels out of the water Hayward Area Recreation and Park District , abbreviated H.A.R.D. Music Hard band , a Hungarian hard rock supergroup Hard Brainpower album Hard Brainpower album Hard Gang of Four album Hard Gang of Four album Hard Jagged Edge album Hard Jagged Edge album Hard song Hard song , by Rihanna Disambig cs Tvrdost de Hard Begriffskl rung fr Hard it Hard nl Hard no Hardhet pt Hard ro Hard uk Hard ... more details
Infobox Album See Wikipedia WikiProject Albums Name Hard For It Type Studio Artist Cutty Ranks Cover Cutty Ranks Hard For It.jpg Released 2006 ref name vibes cite web url http www.reggae vibes.com rev sin hardfori.htm title Cutty Ranks Hard for It Review accessdate 2007 12 30 work Reggae Vibes.com ref Recorded Genre Length Label Walboomers Records ref name vibes Producer Reviews Last album This album Hard For It Next album Hard For It is an album by Cutty Ranks . The song 20 Inch was recorded in several versions, including a version with vocals by Master P . Track listing Talli Talli Remix feat. Kobra Khan What Dem Fighting For Dirty Mind Hard For It 20 Inch Mega Mix feat. Kobra Khan Head Mistress Dem A Eat Gal Strange Feeling Who Give Di Orders Wise Up Better Day Holiday Take Me Away feat. Emereld Guilty feat. A20 Turn Me On feat. Flave I Congratulate You Move To The Gal Dem 20 Inch References references http www.reggae vibes.com rev sin hardfori.htm Reggae Vibes review http www.juno.co.uk products 259011 01.htm entry at Juno.uk.co Category 2006 albums Category Cutty Ranks albums ... more details
Use British English date May 2011 Use dmy dates date May 2011 Infobox album Name It s Hard Type studio Artist The Who Cover The who its hard album.jpg Released 4 September 1982 Recorded June 1982, Turn Up Down Studio at Glyn Johns home in Surrey , England Genre Rock music Rock Length 46 29 Language English language English Label Polydor Records Polydor UK br Warner Bros. Records Warner Bros. Original ... It s Hard br 1982 Next album Endless Wire The Who album Endless Wire br 2006 Misc Singles Name It s Hard ... date 1982 Single 3 It s Hard Single 3 date 1983 Album reviews rev1 Allmusic rev1score Rating 2 5 ref ... url http www.rollingstone.com music reviews album 3045 22014 title It s Hard & 124 Album Reviews publisher Rolling Stone date 1982 09 30 accessdate 2012 02 25 ref noprose yes It s Hard is the tenth ..., and finish by saying the album s name It s Hard . Live performances Just over half of this album ... also came during the same concert with the last performance of Athena . It s Hard was played the entire ... played once, on 6 October 1982 at the Rosemont Horizon in Chicago , in place of It s Hard . This was because ... 3 39 Cooks County 3 51 It s Hard 3 47 Dangerous Entwistle 3 36 Eminence Front 5 39 Side two li value ... reissue of It s Hard added four live tracks recorded on the last show of The Who s The Who Tour 1982 1982 tour , on 17 December in Toronto . li value 13 It s Hard 4 56 Eminence Front 5 37 Dangerous ..., and Keith Moon It s Hard Bot generated title ref style text align center 28 UK Singles Chart ... center 38 Eminence Front Billboard Mainstream Rock ref name multiple style text align center 5 It s Hard ... It s Hard artist The Who award Gold autocat yes region United States type album certification Table Bottom format 2col References Reflist External links http www.thewho.net linernotes It sHard.htm It s Hard ... Category Warner Bros. Records albums cs It s Hard de It s Hard es It s Hard fr It s Hard it It s Hard nl It s Hard nn It s Hard pt It s Hard ro It s Hard fi It s Hard sv It s Hard ... more details
Measure or sometimes The Measure in typography refers to the width of a block or Column typography column of text from the left Margin typography margin to the right margin. Punctuation should preferably Hanging punctuation hang outside the measure. It is relative to each design , but can be used as a unit of measurement within that design to create unity and harmony. The measure of a text influences legibility. Long lines are hard to read, short lines are more easily read. 45 75 characters per line are regarded as the ideal range for the measure. For multiple column setups, 40 50 characters are often preferred. 66 is sometimes considered ideal for one column setups. Generally, if the measure is wide, the leading of a text should be increased if the measure is short, it is can safely be decreased. Reverse text, i.e. white text on black also requires more leading. ref http webtypography.net Rhythm and Proportion Horizontal Motion 2.1.2 ref ref http www.markboulton.co.uk journal comments five simple steps to better typography ref The measure or the length of a legible line is the length of the alphabet Caps, Lowercase and Numerals of a typeface of a size being used. References Reflist Typography terms DEFAULTSORT Measure Typography Category Page layout ... more details
In mathematics , Banach measure in measure theory may mean a real valued function on the algebra of all sets for example, in the plane , by means of which a rigid, finitely additive area can be defined for every set, even when a set does not have a true geometric area. That is, this is a theoretical definition getting round the phenomenon of non measurable set s. However, as the Vitali set shows, it cannot be countably additive. The existence of Banach measures proves the impossibility of a Banach Tarski paradox in two dimensions. clarify date October 2011 fact date October 2011 The concept of Banach measure is to be distinguished from the idea of a measure taking values in a Banach space , for example in the theory of spectral measure s. External links http www groups.dcs.st and.ac.uk history Mathematicians Banach.html Stefan Banach bio Category Measures measure theory mathanalysis stub ... more details
Infobox Film name To Be and To Have br small tre et avoir small image ToBeAndToHave.jpg caption director Nicolas Philibert producer Gilles Sandoz writer narrator starring Georges Lopez music Philippe Hersant cinematography Laurent Didier br Katell Djian br Hugues Gemignani br Nicolas Philibert editing Nicolas Philibert distributor released May 19, 2002 runtime 104 minutes country Film France language French budget gross 15,486,840 preceded by followed by To Be and To Have lang fr tre et avoir is a 2002 France French documentary film directed by Nicolas Philibert about a small rural school. It was nominated as an Out of Competition film at the 2002 Cannes Film Festival ref name festival cannes.com cite web url http www.festival cannes.com en archives ficheFilm id 3158545 year 2002.html title Festival de Cannes To Be and to Have accessdate 2009 11 03 work festival cannes.com ref and achieved commercial success. ref name guardian 04 10 03 cite news url http www.guardian.co.uk world 2004 oct 03 film.france publisher The Guardian author Amelia Gentleman title Film s fallen hero fights on for his ... as to be and to have , the two auxiliary verb s in the French language . It is about a primary school ... warned that if Lopez had been successful it would have spelt the death of the documentary, undermining ... purposes. They said it would have a restricted screening, and never discussed marketing the film ... of Lopez, with one newspaper carrying the headline To be and to have the teacher would rather have. However Lopez said money was never his motivation I m simply trying to make the film company ... children have been teased at their new secondary schools because of their involvement. All have ... 265268 To Be and to Have rotten tomatoes id to be and to have title To Be and to Have metacritic film id to be and to have title To Be and to Have mojo title id tobeandtohave title To Be and to Have CinemaofFrance DEFAULTSORT To Be And To Have Category 2002 films Category French documentary films ... more details
multiple issues review March 2010 context March 2010 To Have or to Be? is a book by Erich Fromm that differentiates between having and being. Fromm mentions how the modern society has become Materialism materialistic and prefers having than being . He mentions the great promise of unlimited happiness, Free will freedom , material abundance, and domination of nature. These hopes got to their highs when the industrial age begun. One could feel that there would be unlimited production and hence unlimited consumption. The human beings including men and women have started dreaming about becoming the Gods of earth, but it wasn t really the case. The great promise failed due to the unachievable aims of life, i.e. maximum pleasure and fulfillment of every desire radical hedonism , and the egotism , selfishness and greed of the people. In the industrial age, the development of this economic system was no longer determined by the question that what is good for man, rather what is good for the growth of the system. So, the economic system of society served people in such a way in which only their personal interests were intended to impart. The people having unlimited needs and desires like the Roman empire Roman emperors , the English and French Nobility noblemen were the people who got the most out it. The society nowadays has completely deviated from its actual path. The materialistic nature of people of having has been more developed than being . The modern industrialization has made great promises, but all these promises are developed to fulfill their interests and increase their possession s. In every mode of life, the people should ponder more on being nature and not towards the having nature. This is the truth which people deny and thus the people of modern world have completely lost their inner selves. The point of being is more important as everyone is mortal, and thus having ... thinkers fromm.htm infed.org See also Post materialism DEFAULTSORT To Have Or To Be? Category ... more details
cases also in probability theory are Radon measure s. Radon measures have an alternative definition ... n N , let math E n n, infty subseteq textbf R math which all have infinite Lebesgue measure ... take uncountably many such sets to cover the entire real line. The finite measure spaces have some ... that a measure space may have uncountable measure . Completeness Main Complete measure A measurable ... to have a measure whose values are not restricted to the non negative reals or infinity. For instance ...Image Measure illustration.png right thumb Informally, a measure has the property of being monotone function monotone in the sense that if A is a subset of B , the measure of A is less than or equal to the measure of B . Furthermore, the measure of the empty set is required to be 0. In mathematical analysis , a measure on a set mathematics set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as the size of the subset. In this sense, a measure is a generalization ... measure on a Euclidean space , which assigns the conventional length , area , and volume ..., the Lebesgue measure of the Interval mathematics interval 0, 1 in the real line real numbers is its length in the everyday sense of the word, specifically 1. To qualify as a measure see ... size to each subset of a given set and also satisfy the other axioms of a measure. This problem was resolved by defining measure only on a sub collection of all subsets the subsets on which the measure ... space, on which the Lebesgue measure cannot be defined consistently, are necessarily complicated ... consequence of the axiom of choice . Measure theory was developed in successive stages during ... theory, specifying a measure allows one to define integral s on spaces more general than subsets of Euclidean space moreover, the integral with respect to the Lebesgue measure on Euclidean spaces ... whose probability is given by the measure. Ergodic theory considers measures that are invariant ... more details
Infobox Film name To Have or Not to Have producer Abbas Kiarostami director Niki Karimi writer Niki Karimi released 2001 runtime 45 minutes country Film Iran language Persian language Persian with English language English subtitles To Have or Not to Have Dashtan Va Nadashtan is a 2001 in film 2001 documentary film . It was the first writing and directorial effort of Niki Karimi . See also Niki Karimi Abbas Kiarostami Cinema of Iran External links http www.harvardfilmarchive.org calendars 01novdec iranian.html Review CinemaofIran Category 2001 films Category Iranian films Category Directorial debut films Category Films directed by Niki Karimi Category 2000s drama films 2000s drama film stub Iran film stub tg ... more details
Refimprove date October 2010 In mathematics , a complete measure or, more precisely, a complete measure space is a measure mathematics measure space in which every subset of every null set is measurable having measure zero . More formally, X , , is complete if and only if math S subseteq ... can be illustrated by considering the problem of product spaces. Suppose that we have already constructed Lebesgue measure on the real line denote this measure space by R , B , . We now wish to construct some two dimensional Lebesgue measure sup 2 sup on the plane R sup 2 sup as a product measure . Na vely, we would take the sigma algebra &sigma algebra on R sup 2 sup to be B ... × A sub 2 sub for A sub i sub B . While this approach does define a measure ... measure zero, math lambda 2 0 times A lambda 0 cdot lambda A 0 math for any subset A of R . However ... . Then the sup 2 sup measure of 0 × A is not defined, but math 0 times A subseteq 0 times mathbb R , math and this larger set does have sup 2 sup measure zero. So, this two dimensional Lebesgue measure as just defined is not complete, and some kind of completion procedure is required. Construction of a complete measure Given a possibly incomplete measure space X , , , there is an extension X , sub 0 sub , sub 0 sub of this measure space that is complete ... of the measure space. The completion can be constructed as follows let Z be the set of all subsets of measure zero subsets of X intuitively, those elements of Z that are not already in are the ones ... Then X , sub 0 sub , sub 0 sub is a complete measure space, and is the completion of X ... B mu A . math Examples Borel measure as defined on the Borel algebra generated by the Open set open ... must be used to define the complete Lebesgue measure. n dimensional Lebesgue measure is the completion ... of the Borel measure, as in the one dimensional case. References SpringerEOM title Complete measure ... more details
for the movie adaption To Have and Have Not film infobox Book See Wikipedia WikiProject Novels or Wikipedia WikiProject Books name To Have and Have Not title orig translator image File To Have and Have Note Hemmingway novel 1st edition cover.jpg thumb author Ernest Hemingway cover artist country United States language English series genre Fiction publisher Charles Scribner s Sons release date 1937 pages preceded by followed by To Have and Have Not is a 1937 novel by Ernest Hemingway about Harry Morgan, a fishing boat captain who runs contraband between Cuba and Florida . The novel depicts Harry as an essentially good man who is forced into blackmarket activity by economic forces beyond his control. Initially, his fishing charter customer Mr. Johnson tricks Harry by slipping away without paying ... residents of Key West who are referred to as Conch s. To Have and Have Not is Hemingway s second ... and 1937, and revised as he travelled back and forth from the Spanish Civil War , To Have and Have ... in Mast, p.243. ref Background and publication history To Have and Have Not began as a short ... To Have and Have Not is Hemingway s only novel set in the United States. Written sporadically between 1935 and 1937, and revised as he travelled back and forth from the Spanish Civil War, To Have and Have ..., and received mixed critical reception. ref name Meyers pp292 296 To Have and Have Not was published ... name Oliver, p. 327 Film adaptations To Have or Have Not was adapted to film in 1944, starring Humphrey Bogart and Lauren Bacall . ref cite web author title To Have and Have Not url http www.imdb.com ... To Have and Have Not film To Have and Have Not , directed by Howard Hawks , changed the story ... as a charismatic villain. Pauline Kael and Bosley Crowther have claimed that the ending was used for John ... into The Gun Runners 1958 . ref cite book last Kael first Pauline chapter To Have and Have Not title ... Collection.aspx Hemingway Archives , John F. Kennedy Library Hemingway DEFAULTSORT To Have And Have ... more details
In mathematics specifically, measure theory , a Radon measure , named after Johann Radon , is a measure mathematics measure on the sigma algebra &sigma algebra of Borel set s of a Hausdorff topological space X that is Locally finite measure locally finite and Inner regular measure inner regular . Motivation A common problem is to find a good notion of a measure on a topological space that is compatible with the topology in some sense. One way to do this is to define a measure on the Borel set s of the topological space. In general there are several problems with this for example, such a measure may not have a well defined support measure theory support . Another approach to measure theory is to restrict ... support some authors use this as the definition of a Radon measure . This produces a good theory with no pathological ... to all Hausdorff topological spaces. The idea of the definition of a Radon measure is to find ... functionals, and use these properties as the definition of a Radon measure on an arbitrary Hausdorff space. Definitions We let m be a measure on the &sigma algebra of Borel sets of a Hausdorff topological space X . The measure m is called inner regular or tight if m B is the supremum of m K for K a compact set contained in the Borel set B . The measure m is called outer regular if m B is the infimum of m U for U an open set containing the Borel set B . The measure m is called locally finite if every point has a neighborhood of finite measure. The measure m is called a Radon measure if it is inner ... the underlying measure space is a locally compact topological space, the definition of a Radon measure ... it possible to develop measure and integration in terms of functional analysis , an approach taken ... limit topology induced by the spaces math mathcal K X,K math . If m is a Radon measure on math X ... K X math arises as integration with respect to a Radon measure and is thus a continuous positive linear form on math mathcal K X math . A real valued Radon measure is defined to be any continuous linear ... more details
In mathematics , signed measure is a generalization of the concept of measure mathematics measure by allowing it to have negative and positive numbers negative values. Some authors may call it a charge ... different concepts of a signed measure, depending on whether or not one allows it to take infinite ... signed measure is a function mathematics function math mu Sigma to mathbb R cup infty, infty math ... is that any extended signed measure can take as value, or it can take &minus as value, but both are not available ... operations Extended real number line and must be avoided. A finite signed measure is defined in the same ... addition, which makes them rather hard to work with. On the other hand, measures are extended signed measures, but are not in general finite signed measures. Examples Consider a nonnegative measure ... signed measure is given by math mu A int A f x , d nu x math for all A in . This signed measure takes only finite values. To allow it to take as a value, one needs to replace the assumption ... of f . Properties What follows are two results which will imply that an extended signed measure is the difference of two nonnegative measures, and a finite signed measure is the difference of two finite non negative measures. The Hahn decomposition theorem states that given a signed measure , there exist ... sup sup sup sup . The measure sup sup sup sup is called the variation of , and its ... The sum of two finite signed measures is a finite signed measure, as is the product of a finite signed measure by a real number they are closed under linear combination . It follows that the set of finite signed measures on a measure space X , is a real vector space this is in contrast to positive ... Complex measure Spectral measure Vector measure Riesz representation theorem Total variation Notes .... title Measure theory place Boston&ndash Basel&ndash Stuttgart publisher Birkh user Verlag origyear ... frontcover&dq Measure theory Cohn&cd 1 v onepage&q&f false doi zbl 0436.28001 isbn 3 7643 3003 1. Citation ... more details
dimension math d math have zero or infinite math d math dimensional Hausdorff measure. For example ... Hausdoff measure is zero. In order to measure the size of such sets, mathematicians have considered ...In mathematics a Hausdorff measure is a type of outer measure , named for Felix Hausdorff , that assigns ... Hausdorff measure is the number of points in the set if the set is finite or if the set is infinite. The one dimensional Hausdorff measure of a simple curve in R sup n sup is equal to the length of the curve. Likewise, the two dimensional Hausdorff measure of a Lebesgue measure Construction of the Lebesgue measure measurable subset of R sup 2 sup is proportional to the area of the set. Thus, the concept of the Hausdorff measure generalizes counting, length, and area. It also generalizes ... an integer. These measures are fundamental in geometric measure theory . They appear naturally ... It can be seen that math H d S math is an outer measure more precisely, it is a metric outer measure . By general theory, its restriction to the field of Outer measure Formal definitions Caratheodory measurable sets is a measure. It is called the math d math dimensional Hausdorff measure of math S math . Due to the metric outer measure property, all Borel subset Borel subsets of math X math ..., they may be taken to be open or closed, and will yield the same measure, although the approximations ... to balls gives a different measure. Citation needed date August 2010 Properties of Hausdorff measures Note that if d is a positive integer, the d dimensional Hausdorff measure of R sup d sup is a rescaling of usual d dimensional Lebesgue measure math lambda d math which is normalized so that the Lebesgue measure of the unit cube 0,1 sup d sup is 1. In fact, for any Borel set E , math lambda ... d frac pi d 2 Gamma frac d 2 1 . math Remark . Some authors adopt a definition of Hausdorff measure ... that Hausdorff d dimensional measure in the case of Euclidean space coincides exactly with Lebesgue ... more details
For the record label of the same name Crammed Discs Made to measure typically refers to clothing that is sewn from a standard sized base pattern. A tailored suit is a common example of a made to measure garment. The fit of a made to measure garment is expected to be superior to that of a ready to wear ... customer, while made to measure garments are constructed to fit each customer individually. However, made to measure items are seen by many to involve less workmanship than bespoke or custom made garments, as made to measure garments always involve some form of standardization in the patterning ... s specifications. Typically, a made to measure garment will be more expensive than ready to wear garment but cheaper than a bespoke one. Overview To order a made to measure garment, the customer s measurements are first taken by a made to measure retailer. Then a base pattern is selected that most ... to the customer of made to measure clothing are that the garments will be well fitted to the customer s body and the customer may have the opportunity to customize the fabric and detailing. The primary disadvantage of made to measure is that the customer must wait up to several weeks for the garment to be sewn and delivered. A typical price markup for a made to measure item is 15 over the price of its ready to wear counterpart. Citation needed date May 2010 Made to measure retailers often travel .... Unlike bespoke garments, which traditionally involves hand sewing, made to measure manufacturers use both machine and hand sewing. Made to measure also requires fewer fittings than bespoke, resulting in a shorter wait between customer measurement and garment delivery. Made to measure is sometimes ... of made to measure has been somewhat blurred by a ruling of the British Advertising Standards ... between bespoke and made to measure. The ruling established that A made to measure suit would be cut ... to measure. While etymologist Michael Quinion observed that by definition it was legitimate for a tailor ... more details
have size zero. That is indeed true, but only if one replaces the Jordan measure with the Lebesgue ...In mathematics , the Peano Jordan measure also known as the Jordan content is an extension of the notion ..., a triangle , Disk mathematics disk , or parallelepiped . It turns out that for a set to have Jordan measure it should be well behaved in a certain restrictive sense. For this reason, it is now more common to work with the Lebesgue measure , which is an extension of the Jordan measure to a larger class of sets. Historically speaking, the Jordan measure came first, towards the end of the nineteenth century. The Jordan measure is named after its originators, the France French mathematician ... del calcolo infinitesimale , Fratelli Bocca, Torino, 1887. ref Jordan measure of simple sets ... will be called a n dimensional rectangle , or simply a rectangle . One defines the Jordan measure ... define the Jordan measure of S as simply the sum of the measures of the individual rectangles ... the Jordan measure m S as the sum of measures of the disjoint rectangles. One can show that this definition of the Jordan measure of S is independent of the representation of S as a finite union of disjoint ... Jordan measure as math m B sup S subset B m S math and its outer measure as math m B inf S supset ... measurable if the inner measure of B equals the outer measure. The common value of the two measures is then simply called the Jordan measure of B . It turns out that all rectangles open or closed ... Volterra Cantor set fat Cantor set is not. Its inner Jordan measure vanishes, since its complement set theory complement is dense set dense however, its outer Jordan measure does not vanish, since it cannot be less than in fact, is equal to its Lebesgue measure. Also, a bounded open set is not necessarily ... set B the inner Jordan measure of B is the Lebesgue measure of the interior topology interior of B and the outer Jordan measure is the Lebesgue measure of the closure topology closure . ref Cite journal ... more details
In mathematics , an invariant measure is a measure mathematics measure that is preserved by some function mathematics function . Ergodic theory is the study of invariant measures in dynamical systems . The Krylov Bogolyubov theorem proves the existence of invariant measures under certain conditions on the function and space under consideration. Definition Let X , be a measurable space and let f be a measurable function from X to itself. A measure on X , is said to be invariant under f if, for every measurable set A in , math mu left f 1 A right mu A . math In terms of the pushforward measure push forward , this states that f sub sub . The collection of measures usually probability measure s on X that are invariant under f is sometimes denoted M sub f sub X . The collection of ergodic adjective ergodic measures , E sub f sub X , is a subset of M sub f sub X . Moreover, any convex combination of two invariant measures is also invariant, so M sub f sub X is a convex ... map, a measure on X , is said to be an invariant measure if it is an invariant measure for each ... measure for a sequence of random variable s Z sub t sub sub t 0 sub perhaps a Markov chain or the solution ... T sub a sub R R given by math T a x x a. math Then one dimensional Lebesgue measure &lambda is an invariant measure for T sub a sub . More generally, on n dimensional Euclidean space R sup n sup with its usual Borel algebra, n dimensional Lebesgue measure sup n sup is an invariant measure for any ... measure in the first example is unique up to trivial renormalization with a constant factor. This does not have to be necessarily the case Consider a set consisting of just two points math ... probability measure math mu boldsymbol rm S rightarrow boldsymbol rm R math is invariant. Note ... measure References Invariant measures, John Von Neumann, AMS Bookstore, 1999, ISBN 9780821809129 DEFAULTSORT Invariant Measure Category Dynamical systems Category Measures measure theory pl Miara niezmiennicza ... more details
n sup &rsquo s have been normalized to be probability measures, they are all the same measure. Relationship with other measures The relationship of spherical measure to Hausdorff measure on the sphere and Lebesgue measure on the ambient space has already been discussed. Spherical measure has a nice relationship to Haar measure on the orthogonal group . Let O n denote the orthogonal group group action acting on R sup n sup and let &theta sup n sup denote its normalized Haar measure so that &theta ...In mathematics &mdash specifically, in geometric measure theory &mdash spherical measure &sigma sup n sup is the &ldquo natural&rdquo Borel measure on the n sphere n sphere S sup n sup . Spherical measure is often normalized so that it is a probability measure on the sphere, i.e. so that &sigma sup n sup S sup n sup 1. Definition of spherical measure There are several ways to define spherical measure. One way is to use the usual &ldquo round&rdquo or &ldquo arclength &rdquo metric space ... of R sup n 1 sup . Now construct n dimensional Hausdorff measure H sup n sup on the metric space ... also have given S sup n sup the metric that it inherits as a subspace of the Euclidean space R sup n 1 sup the same spherical measure results from this choice of metric. Another method uses Lebesgue measure &lambda sup n 1 sup on the ambient Euclidean space R sup n 1 sup for any measurable subset ... 0 . math The fact that all these methods define the same measure on S sup n sup follows from an elegant result of Christensen all these measures are obviously uniformly distributed measure uniformly ... group that is, when n is 0, 1 or 3 , spherical measure &sigma sup n sup coincides with normalized Haar measure on S sup n sup . Isoperimetric inequality There is an isoperimetric inequality for the sphere with its usual metric and spherical measure see Ledoux & Talagrand, chapter 1 If A ... sub n sub ball with the same &sigma sup n sup measure as A , then, for any r > ... more details
measure theory measures it uses are probability measures. ref name stern A course in mathematics ... Q1AUhivGmyUC&pg PA149 page 149 ref In mathematics, a probability measure is a real valued function defined on a set of events in a probability space that satisfies Measure mathematics measure properties such as countable additivity . ref An introduction to measure theoretic probability by George G ... between a probability measure and the more general notion of measure which includes concepts like area or volume is that a probability measure must assign 1 to the entire probability space ... events by the measure should be the sum of the probabilities of the events, e.g. the value assigned ... measures have applications in diverse fields, from physics to finance and biology. Definition File Probespazio.png thumb 300px A probability measure mapping the probability space for 3 events to the unit interval . The requirements for a function math &mu to be a probability measure on a probability ... the probability measure requirements so long as math P A math is not zero. ref Probability, Random ... notion of Fuzzy measure theory fuzzy measures in which there is no requirement that the fuzzy values ... page 11 ref For instance, a risk neutral measure is a probability measure which assumes that the current ... probability measure that must be used to price assets in a market, then the market .... For instance, although the fundamental concept of a system in statistical mechanics is a measure ... of the system does not always lead to the definition of a probability measure congruence ... measure may be defined for the likelihood that a variant may be permissible for an amino acid ... Borel measure Fuzzy measure Haar measure Martingale measure References Reflist Further reading Probability and Measure by Patrick Billingsley , 1995 John Wiley ISBN 978 0 471 00710 4 Probability & Measure ... Measures measure theory Category Probability theory de Wahrscheinlichkeitsma pl Miara probabilistyczna ... more details
less than n and have positive n dimensional Lebesgue measure. An example of this is the Smith ...In Measure mathematics measure theory , the Lebesgue measure , named after france French mathematician Henri Lebesgue , is the standard way of assigning a measure mathematics measure to subset s of n dimensional Euclidean space . For n 1, 2, or 3, it coincides with the standard measure of length , area ... a Lebesgue measure are called Lebesgue measurable the measure of the Lebesgue measurable set A is denoted by A . Henri Lebesgue described this measure in the year 1901, followed the next year by his ... Paris ref The Lebesgue measure is often denoted dx , but this should not be confused with the distinct ..., and its Lebesgue measure is the length b &minus a . The open interval a , b has the same measure ... and has measure zero . Any Cartesian product of intervals a , b and c , d is Lebesgue measurable, and its Lebesgue measure is b &minus a d &minus c , the area of the corresponding rectangle . The Lebesgue measure of the set of rational numbers in an interval of the line is 0, although the set is Dense ... measure zero. Vitali set s are examples of sets that are non measurable set not measurable with respect to the Lebesgue measure. Their existence relies on the axiom of choice . Properties The Lebesgue measure on R sup n sup has the following properties If A is a cartesian product of interval mathematics ... closed in the sense of Lebesgue measure see the regularity theorem for Lebesgue measure . Lebesgue measure is both Locally finite measure locally finite and Inner regular measure inner regular , and so it is a Radon measure . Lebesgue measure is Strictly positive measure strictly positive on non empty open sets, and so its Support measure theory support is the whole of R sup n sup ... and has the same measure as A . If A is Lebesgue measurable and math delta 0 math , then the dilation ... and has measure math delta n lambda , A . math More generally, if T is a linear transformation ... more details
In mathematics , specifically measure theory , a complex measure generalizes the concept of measure mathematics measure by letting it have complex number complex values. In other words, one allows for sets whose size length, area, volume is a complex number. Definition Formally, a complex measure &mu on a sigma algebra measurable space X ,&Sigma is a function mathematics function math mu Sigma to mathbb C math defined on &Sigma and taking complex values, which is sigma additivity sigma additive that is, for any ... to a complex measure One can define the integral of a complex valued measurable function with respect to a complex measure in the same way as the Lebesgue integral of a real valued measurable function with respect to a measure mathematics non negative measure , by approximating a measurable function ... of integral of a real valued function with respect to a non negative measure. To that end, it is a quick check that the real and imaginary parts &mu sub 1 sub and &mu sub 2 sub of a complex measure &mu are finite valued signed measure s. One can apply the Hahn decomposition theorem Hahn Jordan ..., math int X f , d mu int X Re f , d mu i int X Im f , d mu. math Variation of a complex measure and polar decomposition For a complex measure &mu , one defines its variation , or absolute value ... out that &mu is a non negative finite measure. In the same way as a complex number can be represented in a complex number polar form , one has a polar decomposition for a complex measure There exists ... that the variation is a measure and the existence of the polar decomposition. The space of complex measures The sum of two complex measures is a complex measure, as is the product of a complex measure by a complex number. That is to say, the set of all complex measures on a measure space X , &Sigma ... Riesz representation theorem Signed measure Vector measure External links http mathworld.wolfram.com ComplexMeasure.html Complex measure on MathWorld Category Measures measure theory it Misura complessa ... more details
In mathematics , a Carleson measure is a type of measure mathematics measure on subset s of n dimension al Euclidean space R sup n sup . Roughly speaking, a Carleson measure on a domain is a measure that does not vanish at the boundary topology boundary of when compared to the surface measure on the boundary topology boundary of . Carleson measures have many applications in harmonic analysis and the theory of partial differential equations , for instance in the solution of Dirichlet problems with rough boundary. The Carleson condition is closely related to the bounded linear operator boundedness of the Poisson operator . Carleson measures are named after the Sweden Swedish mathematician Lennart Carleson . Definition Let n N and let R sup n sup be an open set open and hence measurable set measurable set with non empty boundary . Let be a Borel measure on , and let denote the surface measure on . The measure is said to be a Carleson measure if there exists a constant C > 0 such that, for every point p and every radius r > 0, math mu left Omega cap mathbb B r p right leq C sigma left partial Omega cap mathbb B r p right , math where math mathbb B r p left x in mathbb R n left x p mathbb R n r right. right math denotes the open ball of radius r about p . Carleson s theorem on the Poisson operator Let D denote the unit disc in the complex plane C , equipped with some Borel measure . For 1 ... D , denote the Lp space L sup p sup space on D with respect to the measure . Define the Poisson ... frac e i t z e i t z f e i t , mathrm d t. math Then P is a bounded linear operator if and only if the measure ... norm of the measure . If C R is defined to be the infimum of the set of all constants C ... math holds, then the measure is said to satisfy the vanishing Carleson condition if C R ... author Mortini, R. id c120050 title Carleson measure Category Measures measure theory Category Norms ... more details
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