Understaning a problem involving measurable sets of a bounded sequence of measures Hi guys I am trying to understand my problem,
We have a sequence of measureable sets $\{A_n\}$ Where $\sum _{n=1} ^{\infty}m(A_n) < \infty$
Define a set $B= \{x \in \mathbb  R: \# \{ n:x \in A_n \}=\infty \}$
We want to show m(B)=0
My question is what exactly is B. How I am understanding it is the set of x such that the number of x in $E_n$ is infinity many. That does not quite make sense 

$B$ is set of all points which belongs to $A_n$ infinitely often. In other words, $B=\cap_{i=1}^\infty \cup_{k=i}^\infty A_k $ i.e. $B$ is the limsup of $A_n$'s. Now, since $\sum P(A_n) < \infty$, by Borel-Cantelli lemma, you get $P(B)=0$.
