Definition:Uniform Absolute Convergence

Definition
Let $S$ be a set.

Let $(V,\|\cdot\|)$ be a normed vector space.

Let $\left \langle {f_n} \right \rangle$ be a sequence of mappings $f_n: S \to V$.

Then the series $\displaystyle\sum_{n=1}^\infty f_n$ converges uniformly absolutely if the series $\displaystyle\sum_{n=1}^\infty \|f_n\|$ converges uniformly.

Also see

 * Definition:Uniform Convergence
 * Definition:Absolute Convergence
 * Definition:Local Uniform Absolute Convergence
 * Uniform Absolute Convergence Implies Uniform Convergence