Assume that (left(u_{n}ight)_{n in mathbb{N}}) is uniformly integrable. Show that [lim _{k ightarrow infty} frac{1}{k} int max
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Assume that \(\left(u_{n}ight)_{n \in \mathbb{N}}\) is uniformly integrable. Show that
\[\lim _{k ightarrow \infty} \frac{1}{k} \int \max _{n \leqslant k} u_{n} d \mu=0\]
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