Let $A$ be a Lebesgue null set in $\mathbb R$. Can we find a set $B$ with the following properties:

1) $A \subset B$

2) $B$ has measure $0$

3) $B$ is an $F\_{\sigma}$ set (i.e. a countable union of closed sets).

I suppose so because that null sets I had ever seen have been constructed from finite or countable sets or Cantor set.