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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 Almost surely ： ウィキペディア英語版 In probability theory, one says that an event happens almost surely (sometimes abbreviated as a.s.) if it happens with probability one. The concept is analogous to the concept of "almost everywhere" in measure theory. Although in many basic probability experiments there is no difference between ''almost surely'' and ''surely'' (that is, entirely certain to happen), the distinction is important in more complex cases relating to some sort of infinity. For instance, the term is often encountered in questions that involve infinite time, regularity properties or infinite-dimensional spaces such as function spaces. Basic examples of use include the law of large numbers (strong form) or continuity of Brownian paths.The terms almost certainly (a.c.) and almost always (a.a.) are also used. Almost never describes the opposite of ''almost surely'': an event that happens with probability zero happens ''almost never''.==Formal definition==Let (\Omega,\mathcal,P) be a probability space. An event E \in \mathcal happens ''almost surely'' if P()=1. Equivalently, E happens almost surely if the probability of E not occurring is zero: P() = 0. More generally, any event E (not necessarily in \mathcal) happens almost surely if E^C is contained in a null set: a subset of some N\in\mathcal F such that P()=0. The notion of almost sureness depends on the probability measure P. If it is necessary to emphasize this dependence, it is customary to say that the event E occurs P-almost surely or almost surely (). In probability theory, one says that an event happens almost surely (sometimes abbreviated as a.s.) if it happens with probability one. The concept is analogous to the concept of "almost everywhere" in measure theory. Although in many basic probability experiments there is no difference between ''almost surely'' and ''surely'' (that is, entirely certain to happen), the distinction is important in more complex cases relating to some sort of infinity. For instance, the term is often encountered in questions that involve infinite time, regularity properties or infinite-dimensional spaces such as function spaces. Basic examples of use include the law of large numbers (strong form) or continuity of Brownian paths. The terms almost certainly (a.c.) and almost always (a.a.) are also used. Almost never describes the opposite of ''almost surely'': an event that happens with probability zero happens ''almost never''. ==Formal definition== Let $(\backslash Omega,\backslash mathcal,P)$ be a probability space. An event $E\; \backslash in\; \backslash mathcal$ happens ''almost surely'' if $P()=1$. Equivalently, $E$ happens almost surely if the probability of $E$ not occurring is zero: $P()\; =\; 0$. More generally, any event $E$ (not necessarily in $\backslash mathcal$) happens almost surely if $E^C$ is contained in a null set: a subset of some $N\backslash in\backslash mathcal\; F$ such that $P()=0$. The notion of almost sureness depends on the probability measure $P$. If it is necessary to emphasize this dependence, it is customary to say that the event $E$ occurs $P$-almost surely or almost surely $()$. 抄文引用元・出典: フリー百科事典『 almost certainly (a.c.) and almost always (a.a.) are also used. Almost never describes the opposite of ''almost surely'': an event that happens with probability zero happens ''almost never''.==Formal definition==Let (\Omega,\mathcal,P) be a probability space. An event E \in \mathcal happens ''almost surely'' if P()=1. Equivalently, E happens almost surely if the probability of E not occurring is zero: P() = 0. More generally, any event E (not necessarily in \mathcal) happens almost surely if E^C is contained in a null set: a subset of some N\in\mathcal F such that P()=0. The notion of almost sureness depends on the probability measure P. If it is necessary to emphasize this dependence, it is customary to say that the event E occurs P-almost surely or almost surely ().">ウィキペディア（Wikipedia）』 ■almost certainly (a.c.) and almost always (a.a.) are also used. Almost never describes the opposite of ''almost surely'': an event that happens with probability zero happens ''almost never''.==Formal definition==Let (\Omega,\mathcal,P) be a probability space. An event E \in \mathcal happens ''almost surely'' if P()=1. Equivalently, E happens almost surely if the probability of E not occurring is zero: P() = 0. More generally, any event E (not necessarily in \mathcal) happens almost surely if E^C is contained in a null set: a subset of some N\in\mathcal F such that P()=0. The notion of almost sureness depends on the probability measure P. If it is necessary to emphasize this dependence, it is customary to say that the event E occurs P-almost surely or almost surely ().">ウィキペディアで「In probability theory, one says that an event happens almost surely (sometimes abbreviated as a.s.) if it happens with probability one. The concept is analogous to the concept of "almost everywhere" in measure theory. Although in many basic probability experiments there is no difference between ''almost surely'' and ''surely'' (that is, entirely certain to happen), the distinction is important in more complex cases relating to some sort of infinity. For instance, the term is often encountered in questions that involve infinite time, regularity properties or infinite-dimensional spaces such as function spaces. Basic examples of use include the law of large numbers (strong form) or continuity of Brownian paths.The terms almost certainly (a.c.) and almost always (a.a.) are also used. Almost never describes the opposite of ''almost surely'': an event that happens with probability zero happens ''almost never''.==Formal definition==Let (\Omega,\mathcal,P) be a probability space. An event E \in \mathcal happens ''almost surely'' if P()=1. Equivalently, E happens almost surely if the probability of E not occurring is zero: P() = 0. More generally, any event E (not necessarily in \mathcal) happens almost surely if E^C is contained in a null set: a subset of some N\in\mathcal F such that P()=0. The notion of almost sureness depends on the probability measure P. If it is necessary to emphasize this dependence, it is customary to say that the event E occurs P-almost surely or almost surely ().」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.