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The http://en.wikipedia.org/wiki/Weierstrass_M-test" [Broken] states roughly that if you have an infinite series of bounded functions, and the sum of the bounds of all those functions is finite, then your infinite series is a uniformly convergent series.

My question is, can those functions, which are of course real- or complex- valued, be defined on any kind of space? Specifically, instead of the functions being defined on R or R^n, can they be defined on the natural numbers, so that instead of functions you have sequences? Would the theorem still hold in this case? My guess is that it would work, because I don't see anywhere in the proof where assumptions are made about the domain of the functions.

Any help would be greatly appreciated.

Thank You in Advance.

My question is, can those functions, which are of course real- or complex- valued, be defined on any kind of space? Specifically, instead of the functions being defined on R or R^n, can they be defined on the natural numbers, so that instead of functions you have sequences? Would the theorem still hold in this case? My guess is that it would work, because I don't see anywhere in the proof where assumptions are made about the domain of the functions.

Any help would be greatly appreciated.

Thank You in Advance.

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