Problems in Strong Uniform Distribution



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

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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: 20 Apr 2021 07:10
DOI: 10.2478/tmmp-2014-0018
URI: https://livrepository.liverpool.ac.uk/id/eprint/2018939