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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 Minkowski content ： ウィキペディア英語版 Minkowski content The Minkowski content of a set (named after Hermann Minkowski), or the boundary measure, is a basic concept in geometry and measure theory which generalizes to arbitrary measurable sets the notions of length of a smooth curve in the plane and area of a smooth surface in the space. It is typically applied to fractal boundaries of domains in the Euclidean space, but makes sense in the context of general metric measure spaces. It is related to, although different from, the Hausdorff measure. == Definition == Let $\backslash scriptstyle(X,\backslash ,\; \backslash mu,\backslash ,\; d)$ be a metric measure space, where ''d'' is a metric on ''X'' and μ is a Borel measure. For a subset ''A'' of ''X'' and real ε > 0, let : $A\_\backslash varepsilon\; =\; \backslash$ be the ε-''extension'' of ''A''. The lower Minkowski content of ''A'' is given by :$M\_$ *(A) = \liminf_ \frac, and the upper Minkowski content of ''A'' is :$M^$ *(A) = \limsup_ \frac. If ''M'' *(''A'') = ''M'' *(''A''), then the common value is called the Minkowski content of ''A'' associated with the measure μ, and is denoted by ''M''(''A''). 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「Minkowski content」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.