Borel-Cantelli Lemma in Probability

Theorem

Let $\sequence {E_n}$ be an arbitrary countable sequence of events.

Let the sum of the probabilities of $\sequence {E_n}$ be finite.


Then the probability that infinitely many of the events occur is zero.


Proof


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Source of Name

This entry was named for Émile Borel and Francesco Paolo Cantelli.


Sources

  • 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Borel-Cantelli Lemma
  • 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): Borel-Cantelli Lemma
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