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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 layer cake representation ： ウィキペディア英語版 layer cake representation In mathematics, the layer cake representation of a non-negative, real-valued measurable function ''f'' defined on ''n''-dimensional Euclidean space R''n'' is the formula :$f(x)\; =\; \backslash int\_0^\; 1\_\; (x)\; \backslash ,\; \backslash mathrm\; t\; \backslash text\; x\; \backslash in\; \backslash mathbb^,$ where 1''E'' denotes the indicator function of a subset ''E'' ⊆ R''n'' and ''L''(''f'', ''t'') denotes the super-level set :$L(f,\; t)\; =\; \backslash .$ The layer cake representation follows easily from observing that :$1\_(x)\; =\; 1\_(t)$ and then using the formula :$f(x)\; =\; \backslash int\_0^\; \backslash mathrm\; t.$ The layer cake representation takes its name from the representation of the value ''f''(''x'') as the sum of contributions from the "layers" ''L''(''f'', ''t''): "layers"/values ''t'' below ''f''(''x'') contribute to the integral, while values ''t'' above ''f''(''x'') do not. == See also == *Symmetric decreasing rearrangement 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「layer cake representation」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.