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

单词

dominated convergence theorem

释义

dominated convergence theorem

Let fn:R→R be a sequence of (Lebesgue) integrable functions which converge pointwise to f. Suppose further than |fn|≤g for all n where g is integrable. Then f is integrable and

The theorem is not true of Riemann integrals as the Dirichlet function is a pointwise limit of integrable functions which is not itself Riemann integrable.

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