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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 Essential range ： ウィキペディア英語版 Essential range In mathematics, particularly measure theory, the essential range of a function is intuitively the 'non-negligible' range of the function: It does not change between two functions that are equal almost everywhere. One way of thinking of the essential range of a function is the set on which the range of the function is most 'concentrated'. The essential range can be defined for measurable real or complex-valued functions on a measure space. ==Formal definition== Let ''f'' be a Borel-measurable, complex-valued function defined on a measure space $(X,\backslash mathfrak,\backslash mu)$. Then the essential range of ''f'' is defined to be the set: :$\backslash operatorname(f)\; =\; \backslash left\backslash \backslash \; \backslash varepsilon\; >\; 0:\; \backslash mu(\backslash )\; >\; 0\backslash right\backslash \}$ In other words: The essential range of a complex-valued function is the set of all complex numbers ''z'' such that the inverse image of each ε-neighbourhood of ''z'' under ''f'' has positive measure. 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「Essential range」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.