# Talk:Absolutely Convergent Generalized Sum Converges

The proof on User:Lord Farin/Sandbox is half a screen shorter, and avoids misty talk about some set being countable and rather gives a more direct proof. Is it okay to remove the proof that is up here now? Or should I keep them both? --Lord_Farin 18:30, 27 January 2012 (EST)

## Repetition

A quick glance suggests a substantial overlap between the two sections of this proof. I think there is very likely a way to factor that out. One thing that may help: it appears to me that a substantial portion of the first section is essentially showing that given a convergent generalized sum of positive real numbers, there is a series whose terms are drawn from those of the generalized sum and which has the same limit as that generalized sum. --Dfeuer (talk) 19:44, 1 August 2013 (UTC)

## Free generalization

Nothing here uses the premise that the space involved is a vector space, so the proof goes through if it is assumed only to be a complete normed abelian group, rather than a Banach space, unless I'm missing something. --Dfeuer (talk) 20:22, 1 August 2013 (UTC)