“BorelCantelliLemma”的概念、定义、习题解题方法及翻译-数学辞典

单词	BorelCantelliLemma
释义	Borel-Cantelli lemma Let $A_{1},A_{2},\\dots$ be random events in a probability space. 1. If $\\sum_{n=1}^{\\infty}P(A_{n})<\\infty$ , then $P(A_{n}\\operatorname{i.o.})=0$ ; 2. If $A_{1},A_{2},\\dots$ are independent, and $\\sum_{n=1}^{\\infty}P(A_{n})=\\infty$ ,then $P(A_{n}\\operatorname{i.o.})=1$ where $A=[A_{n}\\operatorname{i.o.}]$ represents the event “ $A_{n}$ happens for infinitely many values of $n$ .”Formally, $A=\\limsup A_{n}$ , which is a limit superior of sets.
随便看	face of a convex set FaceOfAConvexSetAlternativeDefinitionOf face of a convex set, alternative definition of FactorEmbeddable factor embeddable Factorial factorial FactorialBase factorial base FactorialBaseRepresentationOfFractions factorial base representation of fractions FactorialModuloPrimePowers factorial modulo prime powers FactorialPrime factorial prime FactoringAllonePolynomialsUsingTheGroupingMethod factoring all-one polynomials using the grouping method FactoringASumOrDifferenceOfTwoCubes factoring a sum or difference of two cubes Factorion factorion FactorizationCriterion factorization criterion FactorizationOfPrimitivePolynomial factorization of primitive polynomial

数学辞典收录了18232条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。

Borel-Cantelli lemma