Let f(x) be a real-valued Lebesgue measurable function on $\displaystyle \mathbb R^n$, show that there exist Borel measurable function g and h such that g(x)=h(x) a.e.[m], and $\displaystyle g(x)\leq f(x)\leq h(x)\text{ for all }x\in \mathbb R^n$.

"a.e.[m]" means " holds almost everywhere with respect to lebesgue measure".

I know this problem is good problem ofr helping us understand the relation between lebesgue and borel measurability. It concerns the completion of Borel measurable set class. And something else.....

Any help will be appreciate.