Talk:Existence of Integral on Union of Adjacent Intervals

Regarding the presentation, I would prefer splitting the statement "$\int = \int + \int$, provided both exist" and the statement "$\int$ exists iff $\int + \int$ exists". I'm not sure whether these should be on the same page, but I'd say they do (perhaps using subpages). This type of proof abounds in measure theory and real analysis, so either we already thought of some good way to present this, or we should do this now so that we can mimic the approach for future applications. &mdash; Lord_Farin (talk) 09:46, 27 April 2015 (UTC)