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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 Kuratowski–Ulam theorem ： ウィキペディア英語版 Kuratowski–Ulam theorem In mathematics, the Kuratowski–Ulam theorem, introduced by , called also Fubini theorem for category, is an analog of the Fubini's theorem for arbitrary second countable Baire spaces. Let ''X'' and ''Y'' be second countable Baire spaces (or, in particular, Polish spaces), and $A\backslash subset\; X\backslash times\; Y$. Then the following are equivalent if ''A'' has the Baire property: # ''A'' is meager (respectively comeager) # The set $\backslash$ is comeager in X, where $A\_x=\backslash pi\_Y(\backslash lbrace\; x\; \backslash rbrace\; \backslash times\; Y)$, where $\backslash pi\_Y$ is the projection onto Y. Even if A does not have the Baire property, 2. follows from 1. Note that the theorem still holds (perhaps vacuously) for X - arbitrary Hausdorff space and Y - Hausdorff with countable π-base. The theorem is analogous to regular Fubini's theorem for the case where the considered function is a characteristic function of a set in a product space, with usual correspondences – meagre set with set of measure zero, comeagre set with one of full measure, a set with Baire property with a measurable set. ==References== * 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「Kuratowski–Ulam theorem」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.