Timeline for Limit of an integral vs limit of the integrand

7 events

when toggle format	what		by	license	comment
May 14, 2019 at 12:03	comment	added	vidyarthi		@NateEldredge or, even dominated/monotone convergence
May 10, 2019 at 22:46	comment	added	Nate Eldredge		Philosophically, you ought to assume that limits don't commute until you can prove that they do, e.g. using uniform convergence.
May 10, 2019 at 21:39	comment	added	jonathan wolf		Thank you very much for your clarifying comment, @CarloBeenakker. The source of my confusion is that I cannot understand why these limits ($\lim_{\alpha\to 0}$ and $\lim_{\varepsilon\to 0}$) don't commute and what strategy should I follow to obtain a result that does not depend on the order I take those limits. The problem is from physics field theory, so that with $\alpha$ being mass of some field, I need to be able to restore the massless limit by setting $\alpha\to0$, as we restore, for instance, the Coulomb potential $1/r$ from the Yukawa $e^{-mr}/r$ simply by letting $m\rightarrow 0$.
May 10, 2019 at 21:04	history	edited	Carlo Beenakker	CC BY-SA 4.0	added 227 characters in body
May 10, 2019 at 20:59	history	edited	Carlo Beenakker	CC BY-SA 4.0	added 227 characters in body
May 10, 2019 at 20:34	history	edited	Carlo Beenakker	CC BY-SA 4.0	added 11 characters in body
May 10, 2019 at 20:27	history	answered	Carlo Beenakker	CC BY-SA 4.0