dominated convergence theorem


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.