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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 Steinhaus theorem ： ウィキペディア英語版 Steinhaus theorem In the mathematical field of real analysis, the Steinhaus theorem states that the difference set of a set of positive measure contains an open neighbourhood of zero. It was first proved by Hugo Steinhaus.〔; 〕 ==Statement== Let ''A'' be a Lebesgue-measurable set on the real line such that the Lebesgue measure of ''A'' is not zero. Then the ''difference set'' : $A-A=\backslash \; \backslash ,$ contains an open neighbourhood of the origin. More generally, if ''G'' is a locally compact group, and ''A'' ⊂ ''G'' is a subset of positive (left) Haar measure, then : $AA^\; =\; \backslash \; \backslash ,$ contains an open neighbourhood of unity. The theorem can also be extended to nonmeagre sets with the Baire property. The proof of these extensions, sometimes also called Steinhaus theorem, is almost identical to the one below. 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「Steinhaus 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.