On the First and the Second Borel-Cantelli Lemmas

Jian-Sheng Xie, Qihang Wang

Let $\{A_n{\}}_{n=1}^{\infty }$ be a sequence of events and let $S:=\sum _{n=1}^{\infty }{1}_{A_n}$. We present in this note equivalent characterizations for the statements $\m…