How to construct a set $E \subseteq \mathbb{R}^n$ satisfying the following two conditions:
(i) $E$ is Lebesgue measurable;
(ii) $E$ is not a Borel set.
(Here a Borel set is a member of Borel $\sigma$-algebra, which is defined by the $\sigma$-algebra generated by the collection of all open sets in $\mathbb{R}^n$.)