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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Fatou lemma ： ウィキペディア英語版 Fatou's lemma In mathematics, Fatou's lemma establishes an inequality relating the integral (in the sense of Lebesgue) of the limit inferior of a sequence of functions to the limit inferior of integrals of these functions. The lemma is named after Pierre Fatou. Fatou's lemma can be used to prove the Fatou–Lebesgue theorem and Lebesgue's dominated convergence theorem. ==Standard statement of Fatou's lemma== Let ''f''1, ''f''2, ''f''3, . . . be a sequence of non-negative measurable functions on a measure space (''S'',''Σ'',''μ''). Define the function ''f'' : ''S'' → () a.e. pointwise limit by :$$ f(s) =\liminf_ f_n(s),\qquad s\in S. Then ''f '' is measurable and :$$ \int_S f\,d\mu \le \liminf_ \int_S f_n\,d\mu\,. Note: The functions are allowed to attain the value +∞ and the integrals may also be infinite. 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「Fatou's lemma」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.