# Talk:Continuity under Integral Sign

If this result is called the "Continuity Lemma" then that what the title of this page ought to be. The "Continuity Under ..." title can be retained as a link to it, but the general evolved style of this site is such that if a theorem / definition has a "name" then we use it.

Thoughts? --prime mover (talk) 22:27, 8 November 2012 (UTC)

Schilling calls it that; cursory web search didn't immediately yield other sources. I'd be tempted to call this "Continuity of Parameter-Dependent Integrals" but that's just way out (we'd have to define "parameter-dependent integral"). My lecture notes for elementary $\epsilon$-$\delta$ calculus mention this under the heading (translated) "Taking limits under the integral sign". The differentiability lemma follows under "Differentiation under the integral sign". Thus Linus's proposal isn't way out. Also, I'd prefer "under" over "Under". --Lord_Farin (talk) 22:42, 8 November 2012 (UTC)