Borel-Cantelli lemma

Let A1,A2, be random events in a probability spaceMathworldPlanetmath.

  1. 1.

    If n=1P(An)<, then P(Ani.o.)=0;

  2. 2.

    If A1,A2, are independentPlanetmathPlanetmath, and n=1P(An)=, then P(Ani.o.)=1

where A=[Ani.o.] represents the event “An happens for infinitely many values of n.” Formally, A=lim supAn, which is a limit superior of sets.

Title Borel-Cantelli lemmaMathworldPlanetmath
Canonical name BorelCantelliLemma
Date of creation 2013-03-22 13:13:18
Last modified on 2013-03-22 13:13:18
Owner Koro (127)
Last modified by Koro (127)
Numerical id 7
Author Koro (127)
Entry type Theorem
Classification msc 60A99