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This topic has appeared in the English Wikipedia rankings 1 time. It first appeared on 2026-05-12 and was most recently seen on 2026-05-12.
The Borel–Cantelli lemma is a result in measure theory. It is often stated in the context of probability theory, where it is used to study whether, in a given sequence of events, a finite or infinite number of these events occur. The statement of the lemma is often split into two parts:The first Borel–Cantelli lemma, which states that if the sum of the probabilities of the events is finite, then the probability that infinitely many of them occur is 0. This result holds for any sequence of events, without additional assumptions;
The second Borel–Cantelli lemma, which states that if the events are independent and the sum of their probabilities is infinite, then the probability that infinitely many of them occur is 1.
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