About: Infinite-dimensional Lebesgue measure

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In mathematics, there is a theorem stating that there is no analogue of Lebesgue measure on an infinite-dimensional Banach space. Other kinds of measures are therefore used on infinite-dimensional spaces: often, the abstract Wiener space construction is used. Alternatively, one may consider Lebesgue measure on finite-dimensional subspaces of the larger space and consider so-called prevalent and shy sets.

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rdf:type	yago:WikicatBanachSpaces yago:WikicatTheoremsInAnalysis yago:Abstraction100002137 yago:Attribute100024264 yago:Communication100033020 yago:Message106598915 yago:Proposition106750804 yago:Space100028651 yago:Statement106722453 yago:Theorem106752293
rdfs:label	Mesure de Lebesgue en dimension infinie (fr) Infinite-dimensional Lebesgue measure (en)
rdfs:comment	In mathematics, there is a theorem stating that there is no analogue of Lebesgue measure on an infinite-dimensional Banach space. Other kinds of measures are therefore used on infinite-dimensional spaces: often, the abstract Wiener space construction is used. Alternatively, one may consider Lebesgue measure on finite-dimensional subspaces of the larger space and consider so-called prevalent and shy sets. (en) En mathématiques, et plus précisément en théorie de la mesure on peut démontrer qu'il n'y a pas d'analogue de la mesure de Lebesgue sur un espace de Banach de dimension infinie. D'autres sortes de mesures peuvent cependant être utilisées dans ce cas, par exemple, la construction d'un (en). Il est également possible de partir de la mesure de Lebesgue sur des sous-espaces de dimension finie, et de considérer certains ensembles analogues aux ensembles de mesure nulle et de leurs complémentaires, les (en). (fr)
dcterms:subject	Banach spaces Articles containing proofs Theorems in analysis Measure theory
Wikipage page ID	6607484 (xsd:integer)
Wikipage revision ID	1119695076 (xsd:integer)
Link from a Wikipage to another Wikipage	Product measure Banach spaces Invariant measure Articles containing proofs Mathematics Measure theory Neighbourhood (mathematics) Separable space Geometry Theorem Pushforward measure Lp space Pairwise disjoint Banach space Topological group Haar measure Lebesgue measure Locally finite measure Euclidean space Hilbert cube Theorems in analysis Abstract Wiener space Measure theory Translation (geometry) Circle group Open set Prevalent and shy sets Trivial measure Strictly positive measure Tychonoff product Open ball Compact set
Link from a Wikipage to an external page	http://projecteuclid.org/euclid.pjm/1102806462%7Cjournal=Pacific
sameAs	Infinite-dimensional Lebesgue measure Infinite-dimensional Lebesgue measure Infinite-dimensional Lebesgue measure Infinite-dimensional Lebesgue measure Infinite-dimensional Lebesgue measure
dbp:wikiPageUsesTemplate	dbt:Cite_journal dbt:Analysis_in_topological_vector_spaces dbt:Functional_analysis
has abstract	In mathematics, there is a theorem stating that there is no analogue of Lebesgue measure on an infinite-dimensional Banach space. Other kinds of measures are therefore used on infinite-dimensional spaces: often, the abstract Wiener space construction is used. Alternatively, one may consider Lebesgue measure on finite-dimensional subspaces of the larger space and consider so-called prevalent and shy sets. Compact sets in Banach spaces may also carry natural measures: the Hilbert cube, for instance, carries the product Lebesgue measure. In a similar spirit, the compact topological group given by the Tychonoff product of infinitely many copies of the circle group is infinite-dimensional, and carries a Haar measure that is translation-invariant. (en) En mathématiques, et plus précisément en théorie de la mesure on peut démontrer qu'il n'y a pas d'analogue de la mesure de Lebesgue sur un espace de Banach de dimension infinie. D'autres sortes de mesures peuvent cependant être utilisées dans ce cas, par exemple, la construction d'un (en). Il est également possible de partir de la mesure de Lebesgue sur des sous-espaces de dimension finie, et de considérer certains ensembles analogues aux ensembles de mesure nulle et de leurs complémentaires, les (en). Toutefois, les compacts d'espaces de Banach peuvent parfois porter des mesures naturelles, ainsi le cube de Hilbert peut être muni de la mesure de Lebesgue produit. De même, le groupe topologique compact obtenu comme produit d'une infinité de copies du cercle unité est de dimension infinie, mais admet une mesure de Haar invariante par translation. (fr)
gold:hypernym	Theorem
prov:wasDerivedFrom	wikipedia-en:Infinite-dimensional_Lebesgue_measure?oldid=1119695076&ns=0
page length (characters) of wiki page	4632 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Infinite-dimensional_Lebesgue_measure
is Link from a Wikipage to another Wikipage of	Besov measure Abstract Wiener space Infinite dimensional Lebesgue measure List of things named after Henri Lebesgue There is no infinite-dimensional Lebesgue measure
is Wikipage redirect of	Infinite dimensional Lebesgue measure There is no infinite-dimensional Lebesgue measure
is foaf:primaryTopic of	wikipedia-en:Infinite-dimensional_Lebesgue_measure

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