# measure theory-Lebesgue measure

• Oct 18th 2012, 12:53 AM
chath
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.
• Oct 21st 2012, 01:56 AM
girdav
Re: measure theory-Lebesgue measure
This can help you (first deal with the case $E$ bounded).