Properties
- If a series of functions into C (or any Banach space) is uniformly absolutely-convergent, then it is uniformly convergent.
- Uniform absolute-convergence is independent of the ordering of a series. This is because, for a series of nonnegative functions, uniform convergence is equivalent to the property that, for any ε > 0, there are finitely many terms of the series such that excluding these terms results in a series with total sum less than the constant function ε, and this property does not refer to the ordering.
Read more about this topic: Uniform Absolute-convergence
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