Definition:Uniform Absolute Convergence of Product/Complex Functions/Definition 2

Definition

Let $X$ be a set.

Let $\sequence {f_n}$ be a sequence of bounded mappings $f_n: X \to \C$.

The infinite product $\ds \prod_{n \mathop = 1}^\infty \paren {1 + f_n}$ converges uniformly absolutely if and only if the series $\ds \sum_{n \mathop = 1}^\infty f_n$ converges uniformly absolutely.