On the Borel-Cantelli Lemma and its Generalization

Chunrong Feng, Liangpan Li, Jian Shen

Let $\{A_n{\}}_{n=1}^{\infty }$ be a sequence of events on a probability space $(\Omega ,\mathcal{F},\mathbf{P})$. We show that if ${\lim }_{m\to \infty }{\sum }_{n=1}^m{w}_n\mathbf{P}(A_n)=\infty$…