Let $\displaystyle E$ be a measurable subset of $\displaystyle \mathbb{R}$ with $\displaystyle m(E) < \infty$ and let $\displaystyle f$ be a real-valued measurable function on $\displaystyle E$. Prove that for any $\displaystyle \epsilon > 0$, there exists a bounded measurable function $\displaystyle g$ on $\displaystyle E$ such that $\displaystyle m(\{x \in E : f(x) \not= g(x)\}) < \epsilon$.

Again, how do I go about doing it? Thanks in advance.