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**poincare4223** Let $\displaystyle (X, \mathcal{B}, \mu)$ be a measure space. Prove that if $\displaystyle (A_n)_{n \geq 1}$ is a sequence in $\displaystyle \mathcal{B}$ with $\displaystyle \sum_{n=1}^{\infty} \mu(A_n)< \infty$ then there exists a set $\displaystyle E$ with $\displaystyle \mu(E)=0$ such that if $\displaystyle x \not \in E$ then $\displaystyle x$ belongs to at most finitely many of the $\displaystyle A_n$'s.

Here, I really don't see how to answer this question. I am really struggling with this one. Any hints on where to start would be appreciated.