approximation simple functions with finite support

Question

Let $f$ be a nonnegative measurable function. I want to prove that there is an increasing sequence of nonnegative simple functions each of which vanishes outside a set of finite measure such that $f=\lim_n \phi_n$. Can someone give me a push in the right direction? I can prove this in the case that the measurable domain is $\mathbb{R}$, but otherwise this is intractable to me.