\begin{definition}[Definition:Locally Uniform Absolute Convergence of Product]
Let $X$ be a topological space.
Let $\struct {\mathbb K, \norm {\,\cdot\,} }$ be a valued field.
Let $\sequence {f_n}$ be a sequence of mappings $f_n: X \to \mathbb K$.
Then the infinite product $\ds \prod_{n \mathop = 1}^\infty f_n$ '''converges locally uniformly absolutely''' {{iff}} every point of $X$ has a neighborhood on which it converges uniformly absolutely.
\end{definition}