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.
References in periodicals archive ?
invoking once again the Lebesgue dominated convergence theorem, and passing to the limit as n [right arrow] +[infinity], we find that
Therefore, using the dominated convergence theorem, the limit of the above integral as [epsilon] [right arrow] 0 is bounded by C' [H.
By the dominated convergence theorem and the continuity of w', the function (m, c) [right arrow] (1 - [beta])E [R.
Then [for all]j [member of] {1, 2}, by the dominated convergence theorem