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Probability, Hausdorff dimension, and fractional distribution
Published online by Cambridge University Press: 26 February 2010
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§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.
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