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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 Whitney covering lemma ： ウィキペディア英語版 Whitney covering lemma In mathematical analysis, the Whitney covering lemma, or Whitney decomposition, asserts the existence of a certain type of partition of an open set in a Euclidean space. Originally it was employed in the proof of Hassler Whitney's extension theorem. The lemma was subsequently applied to prove generalizations of the Calderón–Zygmund decomposition. Roughly speaking, the lemma states that it is possible to decompose an open set by cubes each of whose diameters is proportional, within certain bounds, to its distance from the boundary of the open set. More precisely: Whitney Covering Lemma Let $\backslash Omega$ be an open non-empty proper subset of $\backslash mathbb^n$. Then there exists a family of closed cubes $\backslash \_j$ such that * $\backslash cup\_j\; Q\_j\; =\; \backslash Omega$ and the $Q\_j$'s have disjoint interiors. * $\backslash sqrt\; l(Q\_j)\; \backslash leq\; \backslash mathrm(Q\_j,\; \backslash Omega^c)\; \backslash leq\; 4\; \backslash sqrt\; l(Q\_j).$ * If the boundaries of two cubes $Q\_j$ and $Q\_k$ touch then $\backslash frac\; \backslash leq\; \backslash frac\; \backslash leq\; 4.$ * For a given $Q\_j$ there exist at most $12^n\; Q\_k$'s that touch it. Where $l(Q)$ denotes the length of a cube $Q$. ==References== * * . * . * . 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「Whitney covering lemma」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.