## 8.2. Uniform Convergence

### Definition 8.2.8: Convergence Almost Everywhere

A sequence

*f*defined on a set_{n}**D***converges*(pointwise or uniformly)*almost everywhere*if there is a set*with Lebesque measure zero such that***S***f*converges (pointwise or uniformly) on_{n}*. We say that***D \ S***f*converges (pointwise or uniformly) to_{n}*f*a.e.