Suppose $A \subset{\mathbb R^{n}}$ and $\epsilon >0$.
(i) Find an open $V\supset{A}$ such that $ m_{n}^{*}(A) \leq m_{n}^{*}(V) \leq m_{n}^{*}(A) + \epsilon $.
(ii) Does $m_{n}^{*}(V\setminus A) < \epsilon$ always hold for the V in part (i)?
I've proven section (i) with $V=\cup_{k} I_{k}$ with $I_{k}$ open rectangles, but I don't know how to prove part (ii). Thank you-