Let A be a Borel set in 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?