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单词 Borel–Cantelli Lemma
释义

Borel–Cantelli Lemma

A general result in measure theory that is a particularly useful application when applied to a probability measure. If {An} is an infinite sequence of measurable sets, where the sum of the measures inline is finite, then the set of points which lie in an infinite number of the sets must have measure zero. If the An are events in a probability space, then the probability that infinitely many of the events occur is zero. A related result shows that if the events are independent and the sum of their probabilities is infinite, then the probability that infinitely many of the events occur is one.

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更新时间:2025/4/29 3:50:28