Suppose $ f_1, f_2, \cdots$ is a collection of measurable functions which satisfy $ \sup_n \int |f_n|^{1 + \gamma}\ d\mu< \infty$ for some $ \gamma > 1$ , and $ \mu$ is a finite measure. I am being asked to show that the $ \{f_n\}$ are uniformly absolutely continuous. That is, for each $ \epsilonRead more