##  [Borel-Cantelli Lemma](/borel-cantelli-lemma) 

  ##  [Borel-Cantelli Lemma](https://puremath.quantumdictionary.io/borel-cantelli-lemma-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A pair of fundamental statements about sequences of events (En) in a probability space: (i) If the sum of probabilities Σ P(En) is finite then the probability that infinitely many of the En occur is zero (first lemma). (ii) If the En are independent and Σ P(En) diverges then infinitely many En occur with probability one (second lemma).