Let $\displaystyle (X, \mathcal{B}, \mu)$ be a measure space and $\displaystyle f : X \rightarrow \mathbb{R}\cup \{ \infty \}$ be a non-negative integrable function. Prove that $\displaystyle \mu (\{ x : f(x)=\infty \}) =0$.

This seems pretty simple. However, I don't know how to prove that a set has measure zero. I know that if it is integrable then the integral is finite. However, I don't see how the set would have to have measure zero right now.