| 翻訳と辞書 |
| Lusin 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.
|
|