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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 theorem ： ウィキペディア英語版 Lusin's theorem In the mathematical field of real analysis, Lusin's theorem (or Luzin's theorem, named for Nikolai Luzin) states that every measurable function is a continuous function on nearly all its domain. In the informal formulation of J. E. Littlewood, "every measurable function is nearly continuous". ==Classical statement== For an interval (), let :$f:()\backslash rightarrow\; \backslash mathbb$ be a measurable function. Then, for every ''ε'' > 0, there exists a compact ''E'' ⊂ () such that ''f'' restricted to ''E'' is continuous and :$\backslash mu\; (\; E\; )\; >\; b\; -\; a\; -\; \backslash varepsilon.\backslash ,$ Note that ''E'' inherits the subspace topology from (); continuity of ''f'' restricted to ''E'' is defined using this topology. 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 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.