Computation of a limit of integrals

Computation of a limit of integrals

Assume that $f$ is in $L^p(B,\mu)$, for every $p>1$, where $\mu$ is a
measure in a ball $B$ of Euclidean space. Let $I_p=(\int_B
(|f|^p)d\mu)^{1/p}$. I would like to find an easy reference of the
following formula $$\lim_{p\to \infty} I_p = \|f\|,$$ where
$\|f\|=\mathrm{ess\,sup} |f(x)|$.