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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 Packing dimension ： ウィキペディア英語版 Packing dimension In mathematics, the packing dimension is one of a number of concepts that can be used to define the dimension of a subset of a metric space. Packing dimension is in some sense dual to Hausdorff dimension, since packing dimension is constructed by "packing" small open balls inside the given subset, whereas Hausdorff dimension is constructed by covering the given subset by such small open balls. The packing dimension was introduced by C. Tricot Jr. in 1982. ==Definitions== Let (''X'', ''d'') be a metric space with a subset ''S'' ⊆ ''X'' and let ''s'' ≥ 0. The ''s''-dimensional packing pre-measure of ''S'' is defined to be :$P\_0^s\; (S)\; =\; \backslash lim\_\; \backslash sup\; \backslash left\backslash \; (B\_i)^s\; \backslash right|\; \backslash begin\; \backslash \_\; \backslash text\; \backslash \backslash \; \backslash text\; \backslash \backslash \; \backslash text\; \backslash leq\; \backslash delta\; \backslash text\; S\; \backslash end\; \backslash right\backslash \}.$ Unfortunately, this is just a pre-measure and not a true measure on subsets of ''X'', as can be seen by considering dense, countable subsets. However, the pre-measure leads to a ''bona fide'' measure: the ''s''-dimensional packing measure of ''S'' is defined to be :$P^s\; (S)\; =\; \backslash inf\; \backslash left\backslash \; S\_j,\; J\; \backslash text\; \backslash right\backslash \},$ i.e., the packing measure of ''S'' is the infimum of the packing pre-measures of countable covers of ''S''. Having done this, the packing dimension dimP(''S'') of ''S'' is defined analogously to the Hausdorff dimension: :$\backslash begin$ \dim_ = \sup \ \\ & 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「Packing dimension」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.