dominated convergence theorem

(redirected from Lebesgue's dominated convergence theorem)
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dominated convergence theorem

[′däm·ə‚nād·əd kən′vər·jəns ‚thir·əm]
(mathematics)
If a sequence {ƒn } of Lebesgue measurable functions converges almost everywhere to ƒ and if the absolute value of each ƒn is dominated by the same integrable function, then ƒ is integrable and lim ∫ ƒ ndm = ∫ ƒ dm.