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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.
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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

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References

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