I need to prove that if $A$ and $B$ are two closed sets in $\mathbb R^n$, then $A + B$ is an $F_\sigma$.
I started by writing out $A$ and $B$ each as an $F_\sigma$ by intersecting each with balls of center $0$ radius $n$, and taking the union, I don't know if that's a good idea.
Any hint is appreciated. Thanks.