## Measure, please help

Let $A \subseteq N$

$f: N -> [0,\infty]$, $f(n)=a_n$

$\mu_d(A)=n, A ~has ~n ~elements$
$\mu_d(A)=+\infty, A ~has ~\infty ~elements$

1. Prove that $\mu_d$ is measure on $P(N)$, and $f$is $\mu_d$ measurable function.

2. Calculate: $\int_N f d\mu_d$