Talk:Egorov's theorem

I can't understand this formulation. It should say, roughly, that the sequence almost everywhere converges uniformly.

Charles Matthews 10:26, 20 Apr 2005 (UTC)

• I don't understand what you are saying. Can you be more specific about what you think the article ought to say? Thanks. NatusRoma 20:50, 22 Apr 2005 (UTC)
• Charles, I don't believe you are right. Egorov's theorem says that pointwise convergence implies that for any e>0, there is a set whose complement has measure at most e, on which convergence is uniform. This isn't the same as uniform convergence almost everywhere. This means there is a nullset, outside of which convergence is uniform. One can't take the intersection of the sets of measure say, 1/n, outside of which convergence is uniform. That intersection is a nullset, but convergence isn't necessarily uniform outside it. This is because the rate of convergence could be different on each of the sets of the sequence. You cam probably work out an example using your favourite example of pointwise convergence which isn't uniform. HTH. Via strass 20:17, 30 April 2007 (UTC)

Help request

Despite my efforts, I was not able to find a copy of the original (in Russian) paper of Pavel Korovkin: all the 1947 collections of the Doklady I was able to find in Italy are lacunary. Can anyone help me? Daniele.tampieri (talk) 21:25, 10 October 2009 (UTC)

The help request above is still valid. Can anyone help me? Daniele.tampieri (talk) 18:10, 3 April 2011 (UTC)

An update: I succeeded in finding the sought paper at the Leninka, jointly with another important paper of G. N. Duboshin on the multidimensional Faa di Bruno's formula. Daniele.tampieri (talk) 09:14, 1 July 2012 (UTC)

Other Egorov's Theorem

There is another theorem which I know as "Egorov's Theorem" that concerns conjugating a pseudodifferential operator by the solution operator of a hyperbolic evolution equation. It is, I believe, fairly widely used in the theory of linear PDEs. See for example:

http://math.unc.edu/Faculty/met/NLIN.pdf

Section 0.9. Can we create some kind of disambiguation page and then have separate "Egorov's Theorem(measure theory)" and "Egorov's Theorem(pseudodifferential operators)" pages? Holmansf (talk) 17:10, 13 January 2012 (UTC)

Hi Holmansf,

the result you cite is a widely used theorem in the theory of ψDOs, therefore I surely support your idea of writing an entry about it. However, I do not know how to proceed correctly in such homonymy cases: try asking to Oleg Alexandrov. He is my favorite admin and he's also a mathematician. Also I advice you to place a announce on the Wikiproject Mathematics talk page, inviting all interested editors to take part to the discussion you started here. Daniele.tampieri (talk) 18:49, 13 January 2012 (UTC)

The new theorem should be at a page such as Egorov's theorem (pseudodifferential operators) or Egorov's theorem on pseudodifferential operators. There are two options for what to do with the current page:

• If consensus is that the phrase "Egorov's theorem" without any context is very likely to refer to the theorem on the present page, then the present page should stay where it is. A hatnote would be added directing users interested on Egorov's theorem on pseudodifferential operators to the other page.
• If consensus is that "Egorov's theorem" without any context is roughly equally likely to refer to his theorem on uniform convergence and his theorem on pseudodifferential operators, then the present page should be moved to Egorov's theorem (measure theory), Egorov's theorem (uniform convergence), Egorov's theorem on uniform convergence, or something like that. A new page named Egorov's theorem would be created; it would be a disambiguation page.

If you want to look at Wikipedia's guidelines on this, see WP:PRIMARYTOPIC.

Not being an analyst, I don't know what "Egorov's theorem" without any context is likely to mean. But those are our options. Ozob (talk) 14:43, 14 January 2012 (UTC)

Well, trying to follow the guideline WP:PRIMARYTOPIC, it should be said that Egorov's theorem in measure theory, named after Dimitri Egorov, is the older one, being proved in 1910 and 1911, while Egorov's theorem in the theory of pseudodifferential operators, named after Yurii Vladimirovich Egorov (see here for a brief profile) is much younger:

• Egorov, Yu. V. (1969), "The canonical transformations of pseudodifferential operators", Uspekhi Matematicheskikh Nauk (in Russian), 24 (5(149)): 235–236, MR 0265748, Zbl 0191.43802 {{citation}}: Cite has empty unknown parameter: |month= (help).

I think the original name should be kept for the older theorem, while the new entry should be named "Egorov's theorem (pseudodifferential operators)", also due to the fact that the former one is cited in (almost?) all textbooks in measure theory. Holmansf, if you agree with me you can start editing the new entry by clicking the redlink above. Daniele.tampieri (talk) 18:57, 14 January 2012 (UTC)

That plan sounds okay to me. I will begin working on the new page at User:Holmansf/Egorov's theorem (pseudodifferential operators) and post it when it's ready. Holmansf (talk) 14:03, 16 January 2012 (UTC)

X or A?

The theorem (as described in the article) starts out with a measure space X, but then concentrates only on the finite measure subset A. Why not just say "Let (A, Sigma, mu) be a measure space with mu(A)< infty , and let (f_n) be a sequence..."? -- 93.82.31.251 (talk) 23:40, 8 December 2016 (UTC)