Let $\displaystyle A \subseteq N$

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

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

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

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