# Computation of a limit of integrals [duplicate]

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 $\|f\|=\mathrm{ess\,sup} |f(x)|$.

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## migrated from mathoverflow.netAug 18 '13 at 13:44

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