About: Kōmura's theorem

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In mathematics, Kōmura's theorem is a result on the differentiability of absolutely continuous Banach space-valued functions, and is a substantial generalization of Lebesgue's theorem on the differentiability of the indefinite integral, which is that Φ : [0, T] → R given by is differentiable at t for almost every 0 < t < T when φ : [0, T] → R lies in the Lp space L1([0, T]; R).

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rdfs:label	Kōmura's theorem (en) Kōmuras sats (sv)
rdfs:comment	In mathematics, Kōmura's theorem is a result on the differentiability of absolutely continuous Banach space-valued functions, and is a substantial generalization of Lebesgue's theorem on the differentiability of the indefinite integral, which is that Φ : [0, T] → R given by is differentiable at t for almost every 0 < t < T when φ : [0, T] → R lies in the Lp space L1([0, T]; R). (en) Inom matematiken är Kōmuras sats ett resultat om differentierbarheten av funktioner över Banachrum. Satsen är en betydlig generalisering av Lebesgues sats som säger att Φ : [0, T] → R definierad som är differentierbar vid t för nästan alla 0 < t < T då φ : [0, T] → R är i Lp-rummet L1([0, T]; R). (sv)
dcterms:subject	Theorems in functional analysis Theorems in measure theory
Wikipage page ID	13213701 (xsd:integer)
Wikipage revision ID	1121312139 (xsd:integer)
Link from a Wikipage to another Wikipage	Derivative Almost everywhere Indefinite integral Theorems in functional analysis Mathematics Theorems in measure theory Lp space Bochner space Banach space Absolute continuity Reflexive space
Link from a Wikipage to an external page	https://archive.org/details/monotoneoperatio00show https://archive.org/details/monotoneoperatio00show/page/n111
sameAs	Kōmura's theorem Kōmura's theorem Kōmura's theorem Kōmura's theorem
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:MathSciNet dbt:Functional_analysis
has abstract	In mathematics, Kōmura's theorem is a result on the differentiability of absolutely continuous Banach space-valued functions, and is a substantial generalization of Lebesgue's theorem on the differentiability of the indefinite integral, which is that Φ : [0, T] → R given by is differentiable at t for almost every 0 < t < T when φ : [0, T] → R lies in the Lp space L1([0, T]; R). (en) Inom matematiken är Kōmuras sats ett resultat om differentierbarheten av funktioner över Banachrum. Satsen är en betydlig generalisering av Lebesgues sats som säger att Φ : [0, T] → R definierad som är differentierbar vid t för nästan alla 0 < t < T då φ : [0, T] → R är i Lp-rummet L1([0, T]; R). (sv)
prov:wasDerivedFrom	wikipedia-en:Kōmura's_theorem?oldid=1121312139&ns=0
page length (characters) of wiki page	1849 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Kōmura's_theorem
is Link from a Wikipage to another Wikipage of	Komura List of theorems Komura's theorem Komura theorem
is Wikipage redirect of	Komura's theorem Komura theorem
is foaf:primaryTopic of	wikipedia-en:Kōmura's_theorem

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