Dominated convergence theorem
In measure theory, Lebesgue's dominated convergence theorem provides sufficient conditions under which almost everywhere convergence of a sequence of functions implies convergence in the L1 norm. Its power and utility are two of the primary theoretical advantages of Lebesgue integration over Riemann integration. In addition to its frequent appearance in mathematical analysis and partial differential equations, it is widely used in probability theory, since it gives a sufficient condition for the convergence of expected values of random variables.
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AntiderivativeBochner's theoremBochner integralBounded convergence theoremBrezis–Lieb lemmaCauchy's integral formulaConditional expectationConvergence in measureConvergence of random variablesDCTDaniell integralDecomposition of spectrum (functional analysis)Direct comparison testDirichlet integralDominated Convergence TheoremDominated convergenceExpected valueExtended real number lineFatou's lemmaFatou–Lebesgue theoremFederico CafieroFinal value theoremFourier inversion theoremGaetano FicheraGiuseppe VitaliGroup algebra of a locally compact groupGrönwall's inequalityHardy spaceHeaviside step functionHenri LebesgueHenstock–Kurzweil integralInitial value theoremIntegral test for convergenceInterchange of limiting operationsItô calculusLaplace transformLaw of large numbersLaw of total expectationLebesgue's dominated convergence theoremLebesgue dominated convergence
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Dominated convergence theorem
In measure theory, Lebesgue's dominated convergence theorem provides sufficient conditions under which almost everywhere convergence of a sequence of functions implies convergence in the L1 norm. Its power and utility are two of the primary theoretical advantages of Lebesgue integration over Riemann integration. In addition to its frequent appearance in mathematical analysis and partial differential equations, it is widely used in probability theory, since it gives a sufficient condition for the convergence of expected values of random variables.
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Dominerade konvergenssatsen fö ...... r funktion, är integrerbar och
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Em teoria da medida, o teorema ...... rados de variáveis aleatórias.
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En matemáticas, el teorema de ...... funcionales como el espacio .
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En mathématiques, et plus préc ...... de l'intégration de Lebesgue.
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In de integraalrekening is een ...... eeds op de Lebesgue-integraal.
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In matematica, il teorema dell ...... rema di convergenza di Vitali.
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In measure theory, Lebesgue's ...... ed values of random variables.
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Lebesgueova věta popřípadě Leb ...... ící záměnu pořadí operací: a .
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Twierdzenie Lebesgue’a o zbież ...... atematyka Henriego Lebesgue’a.
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Теоре́ма Лебе́га о мажори́руем ...... одится к интегралу её предела.
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Dominerade konvergenssatsen fö ...... r funktion, är integrerbar och
@sv
Em teoria da medida, o teorema ...... rados de variáveis aleatórias.
@pt
En matemáticas, el teorema de ...... funcionales como el espacio .
@es
En mathématiques, et plus préc ...... de l'intégration de Lebesgue.
@fr
In de integraalrekening is een ...... eeds op de Lebesgue-integraal.
@nl
In matematica, il teorema dell ...... rema di convergenza di Vitali.
@it
In measure theory, Lebesgue's ...... ed values of random variables.
@en
Lebesgueova věta popřípadě Leb ...... ící záměnu pořadí operací: a .
@cs
Twierdzenie Lebesgue’a o zbież ...... atematyka Henriego Lebesgue’a.
@pl
Теоре́ма Лебе́га о мажори́руем ...... одится к интегралу её предела.
@ru
label
Dominated convergence theorem
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Dominerade konvergenssatsen
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Gedomineerde convergentie
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Lebesgueova věta
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Satz von der majorisierten Konvergenz
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Teorema da convergência dominada
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Teorema de la convergencia dominada
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Teorema della convergenza dominata
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Théorème de convergence dominée
@fr
Twierdzenie Lebesgue’a o zbieżności ograniczonej
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