Definition

Let $(f_{n})$ be a sequence of functions $f_{n} : D \to R$ , and $(M_{n})$ be a sequence of non-negative real numbers If $\exists M_{n} > 0, \forall x \in D, \forall n \in N, (∣ f_{n} (x) ∣ \leq M_{n} \land n = 1 \sum \infty M_{n} < \infty)$ , then $n = 1 \sum \infty f_{n}$ uniformly and absolutely converges on $D$