Fatou's Lemma and Counting Measure

By writting $\mu=\sum\limits_{n\in\mathbb{N}}\delta_n$, where $\delta_n$ is the Dirac measure at $n$, we can show that $\int_Nh d\mu=\sum\limits_nh(n)$ for any positive function $h$ (or any integrable function $h$)