monotone convergence theorem


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monotone convergence theorem

[′män·ə‚tōn kən′vər·jəns ‚thir·əm]
(mathematics)
The integral of the limit of a monotone increasing sequence of nonnegative measurable functions is equal to the limit of the integrals of the functions in the sequence.
References in periodicals archive ?
By using the definition of the Hilbert-Schmidt norm, the monotone convergence theorem, Lemma 1 and formula (5), we obtain
Notice also that, by the monotone convergence theorem,
Courses in complex function theory are often postponed in favor of courses in point set topology and measure theory, they say, so they assume knowledge of these fields, along with calculus of several variables, epsilon-delta arguments, and Lebesgue's dominated and monotone convergence theorems.