Borel–Cantelli lemmaBorel–Cantelli lemma

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…
• 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…
• Lévy's zero–one law
• Kuratowski convergence

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