I'm having trouble with this problem. I was able to show that if a set A is measurable then for every $\epsilon$ $>$ $0$, there exists both an open set $G$ and a closed set $F$ such that $F$ $⊂$ $A$ $⊂$ $G$ and $m($G\F) $<$ $\epsilon$.
But I can't figure out how to do it in the other direction. Any advice?