Definition:Locally Uniform Absolute Convergence of Product

Definition
Let $X$ be a topological space.

Let $\mathbb K$ be a field with absolute value $\left\vert{\, \cdot \,}\right\vert$.

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

Then the infinite product $\displaystyle \prod_{n \mathop = 1}^\infty f_n$ converges locally uniformly absolutely every point of $X$ has a neighborhood on which it converges uniformly absolutely.

Also see

 * Compact Absolute Convergence of Product