“monotone convergence theorem”的概念、定义、习题解题方法及翻译-数学辞典

单词

monotone convergence theorem

释义

monotone convergence theorem

Let fn:R → R, n ≥ 1, be a sequence of Lebesgue integrable functions (see Lebesgue integration) which is increasing—that is, fn + 1 (x) ≥ fn(x) for all n,x—and such that the integrals $inline$ are bounded above. Then there exists an integrable function f such that fn(x) converges to f(x) almost everywhere and

Compare dominated convergence theorem.

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