Talk:Equidistributed sequence

Sound
This sounds like the same thing as a uniform distribution. Can we just redirect this page there? &mdash;Caesura 12:38, 17 Dec 2004 (UTC)


 * NO! Uniform distribution is about random variables.  This is about non-random sequences!  (The first paragraph was incredibly confusing about just that point, but I've fixed it.)  Michael Hardy 18:56, 10 October 2005 (UTC)

merge suggestion - go for it
Hi Mike,

I'm thinking that equidistribution mod 1 should be made into a sbsection of this article ... is taht what you have in mind? linas 23:54, 10 October 2005 (UTC)

I agree with this. Go ahead and do it. --12.222.158.49 05:53, 6 February 2006 (UTC) (Not mike.)

cleanup
After merge cleanup for redundancy, and expert attention. Ste4k 06:12, 15 July 2006 (UTC)

Discrepancy
The discrepancy needs to be defined in this article, and some work done conjointly on Discrepancy theory. Richard Pinch (talk) 07:11, 16 August 2008 (UTC)
 * I've made a start. Richard Pinch (talk) 10:49, 16 August 2008 (UTC)

Another merger
Should Equidistribution theorem be merged into this article? Richard Pinch (talk) 10:49, 16 August 2008 (UTC)

Explanation needed for |...| in the definition
Let (s1, s2, s3, …) be a bounded sequence of real numbers. What is
 * {s1, s2, s3, …}|?

TomyDuby (talk) 01:56, 24 September 2008 (UTC)


 * Do you mean $$\{ s_1,\ldots,s_n \} \cap [c.d]$$? That's the number of elenments in the intersection of the first n elements of the sequence and the closed interval from c to d.  Richard Pinch (talk) 06:33, 24 September 2008 (UTC)


 * Yes, I meant exactly that. Thanks for explanation!
 * TomyDuby (talk) 07:16, 24 September 2008 (UTC)

Problematic Example
I don't think that the following makes sense:

The sequence {αn} is equidistributed mod 1 for almost all values of α.

Clearly all you need do is take any α with modulus less than 1 to see that you get a convergent sequence which doesn't have the equidistributed property? —Preceding unsigned comment added by Thudso (talk • contribs) 09:37, 26 August 2010 (UTC)
 * Almost all provided that α > 1. The result was proven by Koksma in 1935. Spacepotato (talk) 19:17, 28 August 2010 (UTC)

Cleaned up
Hi, I cleaned up this page (the headings were really confusing and unrelated - things related to equidistribution mod 1 were not under equidistribution mod 1, for instance) and added some content. Also, I decided to be bold and merge the article on Weyl's criterion into this page. This is my first serious edit in Wikipedia, any feedback is welcome :) Yoni (talk) 17:16, 21 February 2014 (UTC)

Assessment comment
Substituted at 14:34, 29 April 2016 (UTC)