翻訳と辞書 Words near each other ・ Singuila ・ Singuilucan ・ Singular ・ Singular (band) ・ Singular (software) ・ Singular boundary method ・ Singular cardinals hypothesis ・ Singular control ・ Singular distribution ・ Singular function ・ Singular homology ・ Singular integral ・ Singular integral operators of convolution type ・ Singular integral operators on closed curves ・ Singular isothermal sphere profile ・ Singular measure ・ Singular perturbation ・ Singular point of a curve ・ Singular point of an algebraic variety ・ Singular SA03 ・ Singular solution ・ Singular spectrum analysis ・ Singular submodule ・ Singular term ・ Singular they ・ Singular trace ・ Singular value ・ Singular value decomposition ・ Singulari Nos ・ Singularia Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Singular measure ： ウィキペディア英語版 Singular measure In mathematics, two positive (or signed or complex) measures ''μ'' and ''ν'' defined on a measurable space (Ω, Σ) are called singular if there exist two disjoint sets ''A'' and ''B'' in Σ whose union is Ω such that ''μ'' is zero on all measurable subsets of ''B'' while ''ν'' is zero on all measurable subsets of ''A''. This is denoted by $\backslash mu\; \backslash perp\; \backslash nu.$ A refined form of Lebesgue's decomposition theorem decomposes a singular measure into a singular continuous measure and a discrete measure. See below for examples. ==Examples on R''n''== As a particular case, a measure defined on the Euclidean space R''n'' is called ''singular'', if it is singular in respect to the Lebesgue measure on this space. For example, the Dirac delta function is a singular measure. Example. A discrete measure. The Heaviside step function on the real line, : has the Dirac delta distribution $\backslash delta\_0$ as its distributional derivative. This is a measure on the real line, a "point mass" at 0. However, the Dirac measure $\backslash delta\_0$ is not absolutely continuous with respect to Lebesgue measure $\backslash lambda$, nor is $\backslash lambda$ absolutely continuous with respect to $\backslash delta\_0$: $\backslash lambda\; (\; \backslash \; )\; =\; 0$ but $\backslash delta\_0\; (\; \backslash \; )\; =\; 1$; if $U$ is any open set not containing 0, then $\backslash lambda\; (U)\; >\; 0$ but $\backslash delta\_0\; (U)\; =\; 0$. Example. A singular continuous measure. The Cantor distribution has a cumulative distribution function that is continuous but not absolutely continuous, and indeed its absolutely continuous part is zero: it is singular continuous. 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「Singular measure」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.