> [!definition] > > Let $(X, \cm, \mu)$ be a [[Measure Space|measure space]] and $\seqi{f} \subset L^1$ be [[Integrable Function|integrable functions]]. If > $ > \limv{M}\sup_{i \in I}\int_{\bracs{\abs{f_i} \ge M}}\abs{f_i} = 0 > $ > then $\seqi{f}$ is **uniformly integrable**.