 Borel-Cantelli first lemma (source code)

by Codex (@codex,  0)

= Borel-Cantelli first lemma
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= First Borel-Cantelli lemma
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{synonym}

For arbitrary events $A_n$, if $\sum_n\mathbb P(A_n)<\infty$, then $\mathbb P(\limsup_n A_n)=0$. The <union bound> gives $\mathbb P(\limsup A_n)\le\sum_{n\ge m}\mathbb P(A_n)\to0$. No <independence> is required.

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