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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.

Attributes	Values
rdfs:label	Dominated convergence theorem (en)
rdfs:comment	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. (en)
sameAs	Dominated convergence theorem Dominated convergence theorem
dbp:wikiPageUsesTemplate	dbt:! dbt:= dbt:Cite_book dbt:Cite_web dbt:Mvar dbt:Reflist dbt:Measure_theory
Subject	Articles containing proofs Probability theorems Theorems in real analysis Theorems in measure theory
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Dominated_convergence_theorem?oldid=1072113503&ns=0
Wikipage page ID	351853 (xsd:integer)
page length (characters) of wiki page	12210 (xsd:nonNegativeInteger)
Wikipage revision ID	1072113503 (xsd:integer)
Link from a Wikipage to another Wikipage	Non-measurable set Probability theory Uniform boundedness Uniform integrability 0 Almost everywhere Banach space Monotone convergence theorem Sequence Articles containing proofs Probability theorems Without loss of generality Triangle inequality Complex number Convergence in measure Convergence of random variables Convergent series Henri Lebesgue Vitali convergence theorem Darboux integral Function (mathematics) If and only if Scheffé's lemma Expected value Fatou's lemma Fatou–Lebesgue theorem Harmonic series (mathematics) Infimum and supremum Interval (mathematics) Absolutely integrable function Lebesgue integration Measurable function Measure (mathematics) Measure space Necessity and sufficiency Pointwise convergence Random variable Real number Riemann integral Theorems in real analysis Theorems in measure theory
has abstract	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. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Dominated_convergence_theorem
is Wikipage redirect of	Dominated convergence Bounded convergence theorem Lebesgue's dominated convergence theorem Lebesgue dominated convergence Dominated Convergence Theorem Lebesgue dominated convergence theorem Lebesque's theorem
is Link from a Wikipage to another Wikipage of	Fourier inversion theorem List of theorems Littlewood's three principles of real analysis Local martingale Antiderivative Bochner's theorem Bochner integral Monotone convergence theorem Brezis–Lieb lemma Cauchy's integral formula Giuseppe Vitali Direct comparison test Dirichlet integral Dominated convergence Leibniz integral rule DCT Decomposition of spectrum (functional analysis) List of real analysis topics Conditional expectation Convergence in measure Convergence of random variables Henri Lebesgue Henstock–Kurzweil integral Daniell integral Final value theorem Gaetano Fichera Expected value Extended real number line Fatou's lemma Fatou–Lebesgue theorem Federico Cafiero

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