Wikipedia:Articles for deletion/Khinchin's theorem

The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result was keep in rewritten, disambiguation form. — TKD::Talk 04:31, 8 August 2007 (UTC)[reply]

Khinchin's theorem (edit | talk | history | protect | delete | links | watch | logs | views) – (View log)

There is no such thing as Khinchin's theorem. The trivial property of cdf mentioned in the article has been known long before Khinchin and is not related to Khinchin in any way (Igny 01:08, 2 August 2007 (UTC))[reply]

• This AfD nomination was incomplete. It is listed now. DumbBOT 09:58, 2 August 2007 (UTC)[reply]

• Apparently, there is a "Khinchin theorem" [1] (still better, there exists at least one [2]), but it's just not this one. Tizio 10:09, 2 August 2007 (UTC)[reply]

• Comment. As Tizio correctly points out, there are several theorems that some authors have referred to as "Khinchin's theorem". Notice that the Springerlink above actually refers to two theorems: Khinchin's theorem on the factorization of probability distributions, and Khinchin's theorem on Diophantine approximations. Tizio's second link points to a result commonly known as the strong law of large numbers.

The point is that this particular result (about the inverse of a cdf) is not generally known as "Khinchin's theorem", and to include it in Wikipedia under this title is just wrong. DavidCBryant 11:38, 3 August 2007 (UTC)[reply]

• delete Is this a theorem or a definition? Septentrionalis PMAnderson 19:39, 3 August 2007 (UTC)[reply]
• Delete After reading this, do you have any idea about what Khinchin's theorem is supposed to accomplish? Neither do I. Mandsford 16:56, 4 August 2007 (UTC)[reply]

However that only means that this article needs to be written better. This does not mean that article be deleted. Shabda 14:30, 5 August 2007 (UTC)[reply]

• It's the triviality that any continuous distribution can be made uniform by a change of variable. Septentrionalis PMAnderson 21:31, 5 August 2007 (UTC)[reply]

• Comment Khinchin's theorem is mentioned on Khinchin's constant page. Shabda 14:29, 5 August 2007 (UTC)[reply]
  • That is a completely different theorem; that theorem is the statement in the lead of the article, about the geometric mean of the coefficients of continued fractions. If it were not for the next discovery, we could consider a redirect there. Septentrionalis PMAnderson 21:31, 5 August 2007 (UTC)[reply]
• Comment Is this any way related to [3] Shabda 14:32, 5 August 2007 (UTC)[reply]
  • No. They at least both deal with function theory, but they are not at all related. Septentrionalis PMAnderson 21:31, 5 August 2007 (UTC)[reply]
• Very Weak Keep: We need some more expert input here, I think. I'm in favor of keeping it until it is proven that this is a hoax, non-notable or else. Hope you understand my position; I don't like mistakes in AfDs --Neigel von Teighen 14:34, 5 August 2007 (UTC)[reply]
  • A substub, about a dubious object, strongly ambiguous with four real theorems, counting Tizio's. If there is ever any evidence (as now there is not) that anybody has ever called this Khinchin's theorem, we can create a better one. Septentrionalis PMAnderson 21:31, 5 August 2007 (UTC)[reply]
    • Hmm... MathWorld doesn't give anything related to this. And normally, if a theorem isn't there, then it is likely to be non-notable. But it seems that "Khinchin" can be also spelt "Khintchine". --Neigel von Teighen 09:46, 6 August 2007 (UTC)[reply]
      • • That's the French method of transliterating Russian; a quite normal problem, and Weisstein should have allowed for it. If this shows up on Mathworld or anywhere as "Khintchine's theorem", I will be surprised; but we should then normalize and disambiguate. Septentrionalis PMAnderson 13:23, 6 August 2007 (UTC)[reply]
• Comment I am considering to withdraw this AFD. I am going to put this article into my todo list, eventually I will rewrite it (taking into account the comments from you, thank you). How can I withdraw the Afd? (Igny 21:36, 6 August 2007 (UTC))[reply]

• Keep, but needs to be renamed to whatever is its standard name. Wrong title is not a good reason for deletion. Note to those who say that "it was known long before Khinchin": most mathematical theorems are not named after their discovered ("Stigler's law of eponymy"). I suspect that this result is related to Khinchin's work on metric properties of continuous fractions, but I do not believe that authoritative sources support the name given (as a side note, when I stumbled across this article, it was using a completely unconventional spelling of Khinchin's name). Concerning triviality: yes, to a person with background in mathematical probability the proof may appear banal, although the statement itself is interesting. In fact, the same can be said about Fermat's little theorem or even Cayley's theorem, yet no one would argue that they are not important! Arcfrk 23:05, 6 August 2007 (UTC)[reply]

• Keep disambig version. Original article is too trivial to merit the name of a theorem. --Salix alba (talk) 07:57, 7 August 2007 (UTC)[reply]
• Keep disambig version. Mathmo ^Talk 23:22, 7 August 2007 (UTC)[reply]
• Keep disambig version. — Preceding unsigned comment added by Michael Hardy (talk • contribs)

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.