By sum of two sets I mean $A+B := \{x+y:x \in A \quad y \in B\}$, and there is a tip in a book of real analysis by Zhou Minqiang which says:

“If $A,B$ are Borel sets in $\mathbb{R}^{n}$, $A+B$ may not be a Borel set.”

I want to know some specific examples.(Maybe $\mathbb{R}^{1}$ ?)

Any comments will be helpful.