Problems in Strong Uniform Distribution

Chan, Kwo and Nair, Radhakrishnan (2014) Problems in Strong Uniform Distribution. Tatra Mountains Mathematical Publications, 59 (1). pp. 51-64.

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Official URL: http://dx.doi.org/10.2478/tmmp-2014-0018

Abstract

<jats:title>Abstract</jats:title> <jats:p>In 1923 A. Khinchin asked if given any B ⊆ [0, 1) of positive Lebesgue measure, we have <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/Untitled-2.jpg" /> </jats:alternatives> </jats:inline-formula> #{n : 1 ≤ n ≤ N : {nx} ∈ B} → |B| for almost all x with respect to Lebesgue measure. Here {y} denotes the fractional part of the real number y and |A| denotes the Lebesgue measure of the set A in [0, 1). In 1970 J. Marstrand showed the answer is no. In this paper the authors survey contributions to this subject since then. </jats:p>

Item Type:	Article
Subjects:	?? QA ??
Depositing User:	Symplectic Admin
Date Deposited:	05 Aug 2015 08:27
Last Modified:	17 Dec 2022 01:38
DOI:	10.2478/tmmp-2014-0018
Related URLs:	Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/2018939