About: Weakly measurable function

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In mathematics—specifically, in functional analysis—a weakly measurable function taking values in a Banach space is a function whose composition with any element of the dual space is a measurable function in the usual (strong) sense. For separable spaces, the notions of weak and strong measurability agree.

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rdf:type	yago:WikicatTheoremsInFunctionalAnalysis yago:Abstraction100002137 yago:Communication100033020 yago:Message106598915 yago:Proposition106750804 disease yago:Statement106722453 yago:Theorem106752293
rdfs:label	弱可測関数 (ja) Weakly measurable function (en) 弱可测函数 (zh)
rdfs:comment	In mathematics—specifically, in functional analysis—a weakly measurable function taking values in a Banach space is a function whose composition with any element of the dual space is a measurable function in the usual (strong) sense. For separable spaces, the notions of weak and strong measurability agree. (en) 数学の、特に関数解析学の分野における、あるバナッハ空間に値を取る弱可測関数（じゃくかそくかんすう、英: weakly measurable function）とは、その双対空間の任意の元との合成が通常の（強い）意味での可測関数であるような関数のことを言う。可分空間においては、弱可測性と強可測性の概念は一致する。 (ja) 在数学中，特别是泛函分析中，如果一个在巴拿赫空间中取值的函数与其所在空间的对偶空间中的任意元素的复合是一般（强）意义下的可测函数，则该函数是弱可测函数。对于可分空间，弱可测性和强可测性的概念是一致的。 (zh)
name	Theorem (en)
dcterms:subject	Types of functions Functional analysis Measure theory
Wikipage page ID	14502271 (xsd:integer)
Wikipage revision ID	1119694804 (xsd:integer)
Link from a Wikipage to another Wikipage	Probability space Types of functions Almost surely Complex number Continuous dual space Continuous linear functional Mathematics Separable space Function (mathematics) Function composition Functional analysis Measurable function Measurable space Measure space Banach space Field (mathematics) Random variable Functional analysis Measure theory If and only if Real number B. J. Pettis Borel sigma algebra Random vector
Link from a Wikipage to an external page	https://archive.org/details/monotoneoperatio00show/page/n109 https://archive.org/details/monotoneoperatio00show%7Curl-access=limited%7Cseries=Mathematical
sameAs	Weakly measurable function Weakly measurable function Weakly measurable function Weakly measurable function Weakly measurable function
dbp:wikiPageUsesTemplate	dbt:Annotated_link dbt:Cite_book dbt:Cite_journal dbt:Reflist dbt:Analysis_in_topological_vector_spaces dbt:Functional_analysis dbt:Math_theorem
note	Pettis, 1938 (en)
has abstract	In mathematics—specifically, in functional analysis—a weakly measurable function taking values in a Banach space is a function whose composition with any element of the dual space is a measurable function in the usual (strong) sense. For separable spaces, the notions of weak and strong measurability agree. (en) 数学の、特に関数解析学の分野における、あるバナッハ空間に値を取る弱可測関数（じゃくかそくかんすう、英: weakly measurable function）とは、その双対空間の任意の元との合成が通常の（強い）意味での可測関数であるような関数のことを言う。可分空間においては、弱可測性と強可測性の概念は一致する。 (ja) 在数学中，特别是泛函分析中，如果一个在巴拿赫空间中取值的函数与其所在空间的对偶空间中的任意元素的复合是一般（强）意义下的可测函数，则该函数是弱可测函数。对于可分空间，弱可测性和强可测性的概念是一致的。 (zh)
math statement	A function defined on a measure space and taking values in a Banach space is measurable if and only if it is both weakly measurable and almost surely separably valued. (en)
gold:hypernym	Function
prov:wasDerivedFrom	wikipedia-en:Weakly_measurable_function?oldid=1119694804&ns=0
page length (characters) of wiki page	4282 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Weakly_measurable_function
is Link from a Wikipage to another Wikipage of	Stone's theorem on one-parameter unitary groups Random element Pettis' theorem Pettis measurability theorem Pettis theorem Almost surely separably valued Essentially separably valued Weak measurability Weak random variable Weak random vector
is Wikipage redirect of	Pettis' theorem Pettis measurability theorem Pettis theorem Almost surely separably valued Essentially separably valued Weak measurability Weak random variable Weak random vector
is foaf:primaryTopic of	wikipedia-en:Weakly_measurable_function

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