Let $(X,\Sigma,\mu)$ be a measure space and let ${f_n}_{n\in\mathbb N}$ be a sequence of (measurable) functions $f_n: X\to \mathbb R$. The sequence converges almost uniformly to $f$ if for all $\varepsilon > 0$, there exists a set $A\in \Sigma$ of measure less than $\varepsilon$ such that $f_n$ converges uniformly to $f$ on $X\setminus A$.
Wikidata ID: Q25377974