1. ## measure theory-Lebesgue measure

Let m* be an Lebesgue outer measure on a set X.Show that a subset E of X is measurable if and only if for each epsilon>0 there exist a measurable set F such that F is a subset of E and m*(E/F)<epsilon.

2. ## Re: measure theory-Lebesgue measure

This can help you (first deal with the case $E$ bounded).