Definition:Uniform Absolute Convergence

Definition
Let $S$ be a set.

Let $\struct {V, \norm {\, \cdot \,} }$ be a normed vector space.

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

Then the series $\ds \sum_{n \mathop = 1}^\infty f_n$ converges uniformly absolutely the series $\ds \sum_{n \mathop = 1}^\infty \norm {f_n}$ converges uniformly.

Also see

 * Definition:Uniform Convergence
 * Definition:Absolutely Convergent Series
 * Definition:Normal Convergence
 * Definition:Local Uniform Absolute Convergence


 * Uniform Absolute Convergence Implies Uniform Convergence