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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?

MathNoob
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  • In other words, if such $F$ and $G$ exist, then $A$ is measurable? – Umberto P. Mar 31 '17 at 22:47
  • Use that open and closed sets are measurable and that null-sets are measurable, and finally that countable unions/intersections of measurable sets are measurable. – PhoemueX Apr 01 '17 at 17:34

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