Uniform absolute-convergence

In mathematics, uniform absolute-convergence is a type of convergence for series of functions.

Like absolute-convergence, it has the useful property that it is preserved when the order of summation is changed.

This is not possible for series of nonnegative numbers, however, so the notion of absolute-convergence precludes this phenomenon.

This is impossible for series of nonnegative functions, so the notion of uniform absolute-convergence can be used to rule out these possibilities.

If the topological space is locally compact, these notions are equivalent.