# Existence of a measurable set , $B\supseteq A$ with $\mu^\ast(A)=\mu^\ast(B)$

Let $A\in \mathbf{R}$. How can I show that $\exists$ a measurable set $B\supseteq A$ such that $\mu^\ast(A)=\mu^\ast(B)$?

I know there is a $G_\delta$ set such that $\mu^\ast(A)=\mu^\ast(G)$. Can I take $B$ to the a $G_\delta$?

-
 What measure are you dealing with? If it is Lebesgue measure, and $\mu^*$ means Lebesgue outer measure, then yes, you can. – user1736 Oct 19 '11 at 6:15 the Lebesgue outer measure. – Kuku Oct 19 '11 at 13:35