$f: \mathbb R^n \to \mathbb R$ be Lebesgue measurable , then there is a Borel measurable $g: \mathbb R^n \to \mathbb R$ such that $f=g$ a.e.?

Question

Let $f: \mathbb R^n \to \mathbb R$ be a Lebesgue measurable function , then is it true that there exist a Borel measurable function $g: \mathbb R^n \to \mathbb R$ such that $f=g$ a.e. ?