  Let $\{A_n\}_{n=1}^\infty$ be a sequence of events and let $\displaystyle
S:=\sum_{n=1}^\infty 1_{A_n}$. We present in this note equivalent
characterizations for the statements $\mathbb{P} (S<\infty)=1$ and $\mathbb{P}
(S=\infty)=1$ respectively. These characterizations are of Borel-Cantelli lemma
type and of Kochen-Stone lemma type respectively, which could be regarded as
the most general version of the first and the second Borel-Cantelli Lemmas.
