I've read that given a set $A$ with finite outer measure, where $A \subseteq \mathbb{R}^n$, there exists an open set $G$ s.t. $A \subseteq G$ and $m(G) - m(A) < \epsilon$ for every $\epsilon > 0$.
However, it is not always the case that we have $m(G) - m(A) \leq m(G \setminus A)$. What example is there where this fails?