翻訳と辞書 Words near each other ・ Randonneuring ・ Randonneurs USA ・ Randonnée ・ Randoon ・ Random coil index ・ Random compact set ・ Random coordinate descent ・ Random digit dialing ・ Random Disc Records ・ Random dopant fluctuation ・ Random dot stereogram ・ Random dungeon ・ Random dynamical system ・ Random early detection ・ Random effects model ・ Random element ・ Random Encounter ・ Random encounter ・ Random Encounter (band) ・ Random Encounter (film) ・ Random Encounters ・ Random End ・ Random energy model ・ Random EP (Number 1) ・ Random EP (Number 2) ・ Random Family ・ Random Fibonacci sequence ・ Random field ・ Random forest ・ Random function 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 Random element ： ウィキペディア英語版 Random element In probability theory, random element is a generalization of the concept of random variable to more complicated spaces than the simple real line. The concept was introduced by who commented that the “development of probability theory and expansion of area of its applications have led to necessity to pass from schemes where (random) outcomes of experiments can be described by number or a finite set of numbers, to schemes where outcomes of experiments represent, for example, vectors, functions, processes, fields, series, transformations, and also sets or collections of sets.” The modern day usage of “random element” frequently assumes the space of values is a topological vector space, often a Banach or Hilbert space with a specified natural sigma algebra of subsets.〔V.V. Buldygin, A.B. Kharazishvili. Geometric Aspects of Probability Theory and Mathematical Statistics. – Kluwer Academic Publishers, Dordrecht. – 2000〕 == Definition == Let $(\backslash Omega,\; \backslash mathcal,\; P)$ be a probability space, and $(E,\; \backslash mathcal)$ a measurable space. A random element with values in ''E'' is a function which is $(\backslash mathcal,\; \backslash mathcal)$-measurable. That is, a function X such that for any $B\backslash in\; \backslash mathcal$, the preimage of B lies in $\backslash mathcal$. Sometimes random elements with values in $E$ are called $E$-valued random variables. Note if $(E,\; \backslash mathcal)=(\backslash mathbb,\; \backslash mathcal(\backslash mathbb))$, where $\backslash mathbb$ are the real numbers, and $\backslash mathcal(\backslash mathbb)$ is its Borel σ-algebra, then the definition of random element is the classical definition of random variable. The definition of a random element $X$ with values in a Banach space $B$ is typically understood to utilize the smallest $\backslash sigma$-algebra on ''B'' for which every bounded linear functional is measurable. An equivalent definition, in this case, to the above, is that a map $X:\; \backslash Omega\; \backslash rightarrow\; B$, from a probability space, is a random element if $f\; \backslash circ\; X$ is a random variable for every bounded linear functional ''f'', or, equivalently, that $X$ is weakly measurable. 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「Random element」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.