Definition 21.1.3 (Convergence Almost Everywhere).label Let $(X, \cm, \mu)$ be a measure space, $Y$ be a topological space, $\seq{f_n}$ and $f$ be Borel measurable functions from $X$ to $Y$, then $f_{n} \to f$ almost everywhere/a.e. if there exists a $\mu$-null set $N \in \cm$ such that $f_{n} \to f$ pointwise on $X \setminus N$.