Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-27T21:17:03.183Z Has data issue: false hasContentIssue false
  • English
  • Français

On a metrical theorem of Weyl

Published online by Cambridge University Press:  26 February 2010

R. C. Baker
R. C. Baker
Affiliation:
Royal Holloway College, Egham Hill. Egham, TW20 OEX, Surrey.
Get access

Extract

The following theorem appears in Weyl's famous memoir [3] of 1916.

THEOREM A. Let λ1 ≤ λ2 ≤ … ≤ λn ≤ … be an increasing sequence of positive integers. Suppose that, of the numbers λ1, … λn, the first h1 are equal to each other, then the following h2 and so on, and finally that the last hm coincide. Let hj. If

the sequenceis uniformly distributed (mod 1)for almost all x, in the Lebesgue sense.

Type
Research Article
Information
Mathematika , Volume 22 , Issue 1 , June 1975 , pp. 29 - 33
Copyright
Copyright © University College London 1975

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Chung, K. L.. A course in probability theory (Harcourt, Brace and World. New York, 1968).Google Scholar
2. Davenport, H., Erdös, P. and LeVeque, W. J.. “On Weyl's criterion for uniform distribution” Michigan Math. J., 10 (1963), 311–314.CrossRefGoogle Scholar
3. Weyl, H.. “Über die Gleichverteilung von Zahlen mod Eins”, Math. Ann., 77 (1916), 313–352.CrossRefGoogle Scholar
4. Marstrand, J. M.. “On Khinchin's conjecture about strong uniform distribution”, Proc. Lond. Math. Soc, 21 (1970), 540–56.CrossRefGoogle Scholar