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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's first inequality for convex bodies ： ウィキペディア英語版 Minkowski's first inequality for convex bodies In mathematics, Minkowski's first inequality for convex bodies is a geometrical result due to the German mathematician Hermann Minkowski. The inequality is closely related to the Brunn–Minkowski inequality and the isoperimetric inequality. ==Statement of the inequality== Let ''K'' and ''L'' be two ''n''-dimensional convex bodies in ''n''-dimensional Euclidean space R''n''. Define a quantity ''V''1(''K'', ''L'') by :$n\; V\_\; (K,\; L)\; =\; \backslash lim\_\; \backslash frac,$ where ''V'' denotes the ''n''-dimensional Lebesgue measure and + denotes the Minkowski sum. Then :$V\_\; (K,\; L)\; \backslash geq\; V(K)^\; V(L)^,$ with equality if and only if ''K'' and ''L'' are homothetic, i.e. are equal up to translation and dilation. 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's first inequality for convex bodies」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.