# Jordan measurable sets are Lebesgue measurable

I have to prove that if a set $E$ that is Jordan-measurable, then $E$ is measurable in the sense of Lebesgue. In order to do this, I am required to use that a set is Jordan-measurable iff $bd(E)$ has content (or measure, in this case) zero. (Here $bd$ denotes de boundary of $E$).

I have to find an open set $G$ and closed $F$ such that $F\subset A \subset G$ and $\mu(G-F)<\epsilon$, but I don't know how to start... Any idea?