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Khinchin's conjecture and Marstrand's theorem

Published online by Cambridge University Press:  26 February 2010

R. C. Baker
R. C. Baker
Affiliation:
Royal Holloway College, Englefield Green, Surrey.
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Extract

We begin by introducing some notations which will be used throughout the paper. Let denote a sequence of distinct positive integers. Let B denote a measurable subset of [0, 1) and {x} the fractional part of x. We write

so that f has period 1 on the real line; and we write

for the number of times {mkx} falls in B, minus the expected value of this number (m(B) ≤ Lebesgue measure of B).

Type
Research Article
Information
Mathematika , Volume 21 , Issue 2 , December 1974 , pp. 248 - 260
Copyright
Copyright © University College London 1974

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