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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 Lusin's separation theorem ： ウィキペディア英語版 Lusin's separation theorem In descriptive set theory and mathematical logic, Lusin's separation theorem states that if ''A'' and ''B'' are disjoint analytic subsets of Polish space, then there is a Borel set ''C'' in the space such that ''A'' ⊆ ''C'' and ''B'' ∩ ''C'' = ∅.〔.〕 It is named after Nikolai Luzin, who proved it in 1927.〔.〕 The theorem can be generalized to show that for each sequence (''A''''n'') of disjoint analytic sets there is a sequence (''B''''n'') of disjoint Borel sets such that ''A''''n'' ⊆ ''B''''n'' for each ''n''. 〔 An immediate consequence is Suslin's theorem, which states that if a set and its complement are both analytic, then the set is Borel. == Notes == 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「Lusin's separation 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.