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- Dominated_convergence_theorem abstract "In measure theory, Lebesgue's dominated convergence theorem provides sufficient conditions under which two limit processes commute, namely Lebesgue integration and almost everywhere convergence of a sequence of functions. The dominated convergence theorem does not hold for the Riemann integral because the limit of a sequence of Riemann-integrable functions is in many cases not Riemann-integrable. Its power and utility are two of the primary theoretical advantages of Lebesgue integration over Riemann integration.It is widely used in probability theory, since it gives a sufficient condition for the convergence of expected values of random variables.".
- Dominated_convergence_theorem wikiPageID "351853".
- Dominated_convergence_theorem wikiPageRevisionID "601333314".
- Dominated_convergence_theorem hasPhotoCollection Dominated_convergence_theorem.
- Dominated_convergence_theorem subject Category:Articles_containing_proofs.
- Dominated_convergence_theorem subject Category:Probability_theorems.
- Dominated_convergence_theorem subject Category:Theorems_in_measure_theory.
- Dominated_convergence_theorem subject Category:Theorems_in_real_analysis.
- Dominated_convergence_theorem type Abstraction100002137.
- Dominated_convergence_theorem type Communication100033020.
- Dominated_convergence_theorem type Message106598915.
- Dominated_convergence_theorem type ProbabilityTheorems.
- Dominated_convergence_theorem type Proposition106750804.
- Dominated_convergence_theorem type Statement106722453.
- Dominated_convergence_theorem type Theorem106752293.
- Dominated_convergence_theorem type TheoremsInMeasureTheory.
- Dominated_convergence_theorem type TheoremsInRealAnalysis.
- Dominated_convergence_theorem comment "In measure theory, Lebesgue's dominated convergence theorem provides sufficient conditions under which two limit processes commute, namely Lebesgue integration and almost everywhere convergence of a sequence of functions. The dominated convergence theorem does not hold for the Riemann integral because the limit of a sequence of Riemann-integrable functions is in many cases not Riemann-integrable.".
- Dominated_convergence_theorem label "Dominated convergence theorem".
- Dominated_convergence_theorem label "Gedomineerde convergentie".
- Dominated_convergence_theorem label "Satz von der majorisierten Konvergenz".
- Dominated_convergence_theorem label "Teorema da convergência dominada".
- Dominated_convergence_theorem label "Teorema della convergenza dominata".
- Dominated_convergence_theorem label "Théorème de convergence dominée".
- Dominated_convergence_theorem label "Twierdzenie Lebesgue’a o zbieżności ograniczonej".
- Dominated_convergence_theorem label "Теорема Лебега о мажорируемой сходимости".
- Dominated_convergence_theorem label "優収束定理".
- Dominated_convergence_theorem label "勒贝格控制收敛定理".
- Dominated_convergence_theorem sameAs Lebesgueova_věta.
- Dominated_convergence_theorem sameAs Satz_von_der_majorisierten_Konvergenz.
- Dominated_convergence_theorem sameAs Théorème_de_convergence_dominée.
- Dominated_convergence_theorem sameAs Teorema_della_convergenza_dominata.
- Dominated_convergence_theorem sameAs 優収束定理.
- Dominated_convergence_theorem sameAs 르베그_지배수렴정리.
- Dominated_convergence_theorem sameAs Gedomineerde_convergentie.
- Dominated_convergence_theorem sameAs Twierdzenie_Lebesgue’a_o_zbieżności_ograniczonej.
- Dominated_convergence_theorem sameAs Teorema_da_convergência_dominada.
- Dominated_convergence_theorem sameAs m.01zcw3.
- Dominated_convergence_theorem sameAs Q1067156.
- Dominated_convergence_theorem sameAs Q1067156.
- Dominated_convergence_theorem sameAs Dominated_convergence_theorem.
- Dominated_convergence_theorem wasDerivedFrom Dominated_convergence_theorem?oldid=601333314.
- Dominated_convergence_theorem isPrimaryTopicOf Dominated_convergence_theorem.