About: Bochner space

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In mathematics, Bochner spaces are a generalization of the concept of spaces to functions whose values lie in a Banach space which is not necessarily the space or of real or complex numbers. The space consists of (equivalence classes of) all Bochner measurable functions with values in the Banach space whose norm lies in the standard space. Thus, if is the set of complex numbers, it is the standard Lebesgue space. Almost all standard results on spaces do hold on Bochner spaces too; in particular, the Bochner spaces are Banach spaces for

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rdfs:label	Bochner space (en) ボホナー空間 (ja)
rdfs:comment	数学の分野におけるボホナー空間（ボホナーくうかん、英: Bochner space）とは、必ずしも実数の空間 R あるいは複素数の空間 C とは限らないバナッハ空間に値を取る関数への、Lp空間の概念の一般化である。ボホナー空間 Lp(X) は、バナッハ空間 X に値を取るボホナー可測関数 f で、そのノルム \|\|f\|\|X が通常の Lp 空間に属するようなもの全ての同値類からなる。したがって、X が複素数の集合であるなら、ボホナー空間は通常のルベーグ空間 Lp となる。 Lp 空間に関するほとんど全ての結果は、ボホナー空間についても同様に得られる。特に、ボホナー空間 Lp(X) はに対してバナッハ空間である。 (ja) In mathematics, Bochner spaces are a generalization of the concept of spaces to functions whose values lie in a Banach space which is not necessarily the space or of real or complex numbers. The space consists of (equivalence classes of) all Bochner measurable functions with values in the Banach space whose norm lies in the standard space. Thus, if is the set of complex numbers, it is the standard Lebesgue space. Almost all standard results on spaces do hold on Bochner spaces too; in particular, the Bochner spaces are Banach spaces for (en)
dcterms:subject	Sobolev spaces Partial differential equations Functional analysis
Wikipage page ID	6751583 (xsd:integer)
Wikipage revision ID	1123706566 (xsd:integer)
Link from a Wikipage to another Wikipage	Almost everywhere United States Compact space Mathematics Salomon Bochner Norm (mathematics) Boundary (topology) Equivalence class Total derivative Lp space Sobolev spaces Sobolev space Functional analysis Partial derivative Mathematician Measure space Banach space Lebesgue measure Dual space Partial differential equation Heat equation Hilbert space Interval (mathematics) Partial differential equations Abuse of notation Functional analysis Support (mathematics) Poland Measure zero Weak derivative Bochner measurable Kolmogorov quotient
sameAs	Bochner space Bochner space Bochner space Bochner space Bochner space
dbp:wikiPageUsesTemplate	dbt:Annotated_link dbt:Cite_book dbt:Reflist dbt:Short_description dbt:Analysis_in_topological_vector_spaces dbt:Functional_analysis
has abstract	In mathematics, Bochner spaces are a generalization of the concept of spaces to functions whose values lie in a Banach space which is not necessarily the space or of real or complex numbers. The space consists of (equivalence classes of) all Bochner measurable functions with values in the Banach space whose norm lies in the standard space. Thus, if is the set of complex numbers, it is the standard Lebesgue space. Almost all standard results on spaces do hold on Bochner spaces too; in particular, the Bochner spaces are Banach spaces for Bochner spaces are named for the Polish-American mathematician Salomon Bochner. (en) 数学の分野におけるボホナー空間（ボホナーくうかん、英: Bochner space）とは、必ずしも実数の空間 R あるいは複素数の空間 C とは限らないバナッハ空間に値を取る関数への、Lp空間の概念の一般化である。ボホナー空間 Lp(X) は、バナッハ空間 X に値を取るボホナー可測関数 f で、そのノルム \|\|f\|\|X が通常の Lp 空間に属するようなもの全ての同値類からなる。したがって、X が複素数の集合であるなら、ボホナー空間は通常のルベーグ空間 Lp となる。 Lp 空間に関するほとんど全ての結果は、ボホナー空間についても同様に得られる。特に、ボホナー空間 Lp(X) はに対してバナッハ空間である。 (ja)
prov:wasDerivedFrom	wikipedia-en:Bochner_space?oldid=1123706566&ns=0
page length (characters) of wiki page	4729 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Bochner_space
is Link from a Wikipage to another Wikipage of	Kōmura's theorem Salomon Bochner Lp space Bochner integral Banach bundle Infinite-dimensional vector function List of vector spaces in mathematics Sobolev-Bochner space
is Wikipage redirect of	Sobolev-Bochner space
is known for of	Salomon Bochner
is known for of	Salomon Bochner
is foaf:primaryTopic of	wikipedia-en:Bochner_space

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