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Scheffé’s lemma : ウィキペディア英語版 | Scheffé’s lemma In mathematics, Scheffé's lemma is a proposition in measure theory concerning the convergence of sequences of integrals. It states that, if is a sequence of integrable functions on a measure space that converges almost everywhere to another integrable function , then if and only if . ==Applications== Applied to probability theory, Scheffe's theorem, in the form stated here, implies that almost everywhere pointwise convergence of the probability density functions of a sequence of -absolutely continuous random variables implies convergence in distribution of those random variables.
抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Scheffé’s lemma」の詳細全文を読む
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