Talk:Approximate continuity

In the western literature Luzin is mostly spelled Lusin. Moreover Lusin's theorem is in general used for the following result in classical measure theory: for any (Lebesgue) measurable function $f:E\to \mathbb R$ and any $\varepsilon > 0$ there is a closed subset $F\subset E$ with $\lambda (E\setminus F) <\varepsilon$ such that $f|_F$ is continuous. This is not consistent with the current entry Luzin theorem. I will however take care of this sometimes later. Camillo 08:48, 6 August 2012 (CEST)

But I see near the end of the article: "In the West, the name "Luzin theorem" refers almost always to a result in measure theory; see Luzin criterion." --Boris Tsirelson 12:59, 6 August 2012 (CEST)

Ah, I missed that! So, what I was taught to call Lusin theorem, here seems to be under Luzin-C-property: for the moment I will link that. Some reordering of all the entries named after Luzin seems anyway needed. By the way, what should we do: create redirect pages with the spelling Lusin, or change the name of the current pages and make a redirect for the old Luzin ones?? Camillo 20:55, 6 August 2012 (CEST)

As for me, yes, "Lusin" as the main name, and "Luzin" as a redirect. Also, I'd prefer separate pages for different theorems, even if they all are "Lusin theorem"s. (At least, Wikipedia does this way.) But maybe others disagree. --Boris Tsirelson 21:09, 6 August 2012 (CEST)

So far I have not been able to find the Stepanov-Denjoy theorem (quoted verbatim from the original article) in any reference. Camillo 09:51, 16 August 2012 (CEST)

Found in Federer's book! He credits the theorem to himself, though :-) Camillo 10:02, 16 August 2012 (CEST)