Sum of two closed sets is measurable 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.

If $A$ is closed and $B$ is compact, show that $A+B$ is closed. (Hint: Use sequential compactness.) In general, write $B$ as a countable union of compact sets. If you need more detail, please let me know and I will gladly provide it.
