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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 Discrete measure ： ウィキペディア英語版 Discrete measure In mathematics, more precisely in measure theory, a measure on the real line is called a discrete measure (in respect to the Lebesgue measure) if it is at most concentrated on a countable set. Note that the support need not be a discrete set. Geometrically, a discrete measure (on the real line, with respect to Lebesgue measure) is a collection of point masses. ==Definition and properties== A measure $\backslash mu$ defined on the Lebesgue measurable sets of the real line with values in $(\backslash infty)$ is said to be discrete if there exists a (possibly finite) sequence of numbers : $s\_1,\; s\_2,\; \backslash dots\; \backslash ,$ such that : $\backslash mu(\backslash mathbb\; R\backslash backslash\backslash )=0.$ The simplest example of a discrete measure on the real line is the Dirac delta function $\backslash delta.$ One has $\backslash delta(\backslash mathbb\; R\backslash backslash\backslash )=0$ and $\backslash delta(\backslash )=1.$ More generally, if $s\_1,\; s\_2,\; \backslash dots$ is a (possibly finite) sequence of real numbers, $a\_1,\; a\_2,\; \backslash dots$ is a sequence of numbers in $(\backslash infty)$ of the same length, one can consider the Dirac measures $\backslash delta\_$ defined by : $\backslash delta\_(X)\; =$ \begin 1 & \mbox s_i \in X\\ 0 & \mbox s_i \not\in X\\ \end for any Lebesgue measurable set $X.$ Then, the measure : $\backslash mu\; =\; \backslash sum\_\; a\_i\; \backslash delta\_$ is a discrete measure. In fact, one may prove that any discrete measure on the real line has this form for appropriately chosen sequences $s\_1,\; s\_2,\; \backslash dots$ and $a\_1,\; a\_2,\; \backslash dots$ 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「Discrete 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.