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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 Continuity set ： ウィキペディア英語版 Continuity set In measure theory, a continuity set of a measure ''μ'' is any Borel set ''B'' such that : $$ \mu(\partial B) = 0\,. where $\backslash partial\; B$ is the boundary set of ''B''. For signed measures, one asks that : $$ |\mu|(\partial B) = 0\,. The class of all continuity sets for given measure ''μ'' forms a ring.〔Cuppens, R. (1975) Decomposition of multivariate probability. Academic Press, New York.〕 Similarly, for a random variable ''X'' a set ''B'' is called continuity set if : $$ \Pr(\in \partial B ) = 0, otherwise ''B'' is called the ''discontinuity set''. The collection of all discontinuity sets is sparse. In particular, given any collection of sets with pairwise disjoint boundaries, all but at most countably many of them will be the continuity sets.〔van der Vaart (1998) Asymptotic statistics. Cambridge University Press. ISBN 978-0-521-78450-4. Page 7〕 The continuity set ''C''(''f'') of a function ''f'' is the set of points where ''f'' is continuous. == 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「Continuity 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.