> [!definition] > > Let $(X, \cm, \mu)$ be a [[Measure Space|measure space]] and $\seq{f_n}$ and $f$ be [[Borel Measurable Function|Borel measurable functions]]. The sequence $f_n \to f$ **almost uniformly** if for all $\varepsilon > 0$, there exists $E \in \cm$ such that $\mu(E^c) < \varepsilon$ and $f_n \to f$ [[Uniform Convergence|uniformly]] on $E$.