Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-30T20:58:59.430Z Has data issue: false hasContentIssue false
  • English
  • Français

Probability, Hausdorff dimension, and fractional distribution

Published online by Cambridge University Press:  26 February 2010

R. Kaufman
R. Kaufman
Affiliation:
Department of Mathematics, University of Illinois, Urbana, Illinois.
Get access

Extract

§0. We begin by stating a theorem of Jarník [1]. Let m be a positive integer, 0 < β < m, and Ψ(q) a positive function of integers q > 0. Let E be the set of points (x1, …, xm) for which the inequality

admits infinitely many solutions q ≥ 1. Then, supposing

Jarník proves that E has infinite Hausdorff β-measure.

Type
Research Article
Information
Mathematika , Volume 17 , Issue 1 , June 1970 , pp. 63 - 67
Copyright
Copyright © University College London 1970

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.Jarník, Vojtech, “Über die simultanen diophantischen Approximationen”, Math. Zeit., 33 (1931), 505–543.CrossRefGoogle Scholar