Must the Minkowski sum of a Borel set and a *closed* ball be Borel?
Let $A$ be a Borel set in $\mathbb{R}^n$. Must then $A + B(0,1)$ be Borel? Here $B(0,1)$ is the closed ball centered at $0$ of radius $1$.
I know that Erdos and Stone gave an example of a compact set (it is Cantor) and a $G_\delta$-set, whose Minkowski's sum is not Borel. But can we have an example with one of them being a closed ball?
It is answered at Math Overflow.