Definition:Uniform Absolute Convergence of Product/General Definition/Definition 2

Definition
Let $X$ be a set.

Let $\struct {\mathbb K, \norm{\,\cdot\,}}$ be a valued field.

Let $\left \langle {f_n} \right \rangle$ be a sequence of bounded mappings $f_n: X \to \mathbb K$.

The infinite product $\displaystyle \prod_{n \mathop = 1}^\infty \left({1 + f_n}\right)$ converges uniformly absolutely the series $\displaystyle \sum_{n \mathop = 1}^\infty f_n$ converges uniformly absolutely.