Fubini's theorem on differentiation (original) (raw)
In mathematics, Fubini's theorem on differentiation, named after Guido Fubini, is a result in real analysis concerning the differentiation of series of monotonic functions. It can be proven by using Fatou's lemma and the properties of null sets.
| Property | Value |
|---|---|
| dbo:abstract | In mathematics, Fubini's theorem on differentiation, named after Guido Fubini, is a result in real analysis concerning the differentiation of series of monotonic functions. It can be proven by using Fatou's lemma and the properties of null sets. (en) En mathématiques, le théorème de différentiation de Fubini est un résultat d'analyse réelle, attribué à Guido Fubini, selon lequel toute série de fonctions croissantes qui converge est presque partout dérivable terme à terme. (fr) ( 적분의 순서 변경에 관한 정리에 대해서는 푸비니 정리 문서를 참고하십시오.) 푸비니의 미분 정리(Fubini's theorem on the differentiation of series with monotonic terms, -微分定理)는 실해석학의 정리로, 단조함수의 함수항급수가 수렴할 때 그 미분 연산의 교환 가능성을 보장해 주는 정리이다. (ko) Малая теорема Фубини — это теорема о почленном дифференцировании ряда монотонных функций, которая гласит: Всюду сходящийся ряд монотонных (неубывающих) функций: почти всюду допускает почленное дифференцирование: (ru) |
| dbo:wikiPageID | 31512735 (xsd:integer) |
| dbo:wikiPageLength | 1335 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID | 821334266 (xsd:integer) |
| dbo:wikiPageWikiLink | dbr:Monotonic_function dbr:Derivative dbr:Almost_everywhere dbr:Real_analysis dbc:Theorems_in_measure_theory dbr:Fatou's_lemma dbr:Null_set dbr:Uniform_convergence dbr:Guido_Fubini dbr:Interval_(mathematics) dbc:Theorems_in_real_analysis dbr:Natural_number dbr:Increasing_function |
| dct:subject | dbc:Theorems_in_measure_theory dbc:Theorems_in_real_analysis |
| gold:hypernym | dbr:Result |
| rdf:type | yago:WikicatTheoremsInAnalysis yago:WikicatTheoremsInMeasureTheory yago:WikicatTheoremsInRealAnalysis yago:Abstraction100002137 yago:Communication100033020 yago:Message106598915 yago:Proposition106750804 yago:Statement106722453 yago:Theorem106752293 |
| rdfs:comment | In mathematics, Fubini's theorem on differentiation, named after Guido Fubini, is a result in real analysis concerning the differentiation of series of monotonic functions. It can be proven by using Fatou's lemma and the properties of null sets. (en) En mathématiques, le théorème de différentiation de Fubini est un résultat d'analyse réelle, attribué à Guido Fubini, selon lequel toute série de fonctions croissantes qui converge est presque partout dérivable terme à terme. (fr) ( 적분의 순서 변경에 관한 정리에 대해서는 푸비니 정리 문서를 참고하십시오.) 푸비니의 미분 정리(Fubini's theorem on the differentiation of series with monotonic terms, -微分定理)는 실해석학의 정리로, 단조함수의 함수항급수가 수렴할 때 그 미분 연산의 교환 가능성을 보장해 주는 정리이다. (ko) Малая теорема Фубини — это теорема о почленном дифференцировании ряда монотонных функций, которая гласит: Всюду сходящийся ряд монотонных (неубывающих) функций: почти всюду допускает почленное дифференцирование: (ru) |
| rdfs:label | Théorème de différentiation de Fubini (fr) Fubini's theorem on differentiation (en) 푸비니의 미분 정리 (ko) Малая теорема Фубини (ru) |
| owl:sameAs | freebase:Fubini's theorem on differentiation yago-res:Fubini's theorem on differentiation wikidata:Fubini's theorem on differentiation dbpedia-fa:Fubini's theorem on differentiation dbpedia-fr:Fubini's theorem on differentiation dbpedia-ko:Fubini's theorem on differentiation dbpedia-ru:Fubini's theorem on differentiation https://global.dbpedia.org/id/n77U |
| prov:wasDerivedFrom | wikipedia-en:Fubini's_theorem_on_differentiation?oldid=821334266&ns=0 |
| foaf:isPrimaryTopicOf | wikipedia-en:Fubini's_theorem_on_differentiation |
| is dbo:knownFor of | dbr:Guido_Fubini |
| is dbo:wikiPageWikiLink of | dbr:Guido_Fubini dbr:List_of_theorems |
| is dbp:knownFor of | dbr:Guido_Fubini |
| is foaf:primaryTopic of | wikipedia-en:Fubini's_theorem_on_differentiation |