Let $\displaystyle (X, \mathcal{B}, \mu)$ be a finite measure space and $\displaystyle f$ be a nonnegative measurable function of $\displaystyle X$. For each $\displaystyle A \in \mathcal{B}$, set

$\displaystyle \nu(A)=\int_Af d\mu$.

Verify that it is a finite measure if and only if $\displaystyle f$ is integrable.

I do not see how this if and only if follows. Any hints on this would be great. Thanks in advance.