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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 rectifiable set ： ウィキペディア英語版 rectifiable set In mathematics, a rectifiable set is a set that is smooth in a certain measure-theoretic sense. It is an extension of the idea of a rectifiable curve to higher dimensions; loosely speaking, a rectifiable set is a rigorous formulation of a piece-wise smooth set. As such, it has many of the desirable properties of smooth manifolds, including tangent spaces that are defined almost everywhere. Rectifiable sets are the underlying object of study in geometric measure theory. ==Definition== A subset $E$ of Euclidean space $\backslash mathbb^n$ is said to be $m$-rectifiable set if there exist a countable collection $\backslash$ of continuously differentiable maps :$f\_i:\backslash mathbb^m\; \backslash to\; \backslash mathbb^n$ such that the $m$-Hausdorff measure $\backslash mathcal^m$ of :$E\backslash backslash\; \backslash bigcup\_^\backslash infty\; f\_i\backslash left(\backslash mathbb^m\backslash right)$ is zero. The backslash here denotes the set difference. Equivalently, the $f\_i$ may be taken to be Lipschitz continuous without altering the definition.〔, calls this definition "countably ''m''-rectifiable".〕 A set $E$ is said to be purely $m$-unrectifiable if for ''every'' (continuous, differentiable) $f:\backslash mathbb^m\; \backslash to\; \backslash mathbb^n$, one has :$\backslash mathcal^m\; \backslash left(E\; \backslash cap\; f\backslash left(\backslash mathbb^m\backslash right)\backslash right)=0.$ A standard example of a purely-1-unrectifiable set in two dimensions is the cross-product of the Smith-Volterra-Cantor set times itself. 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「rectifiable set」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.