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Points of middle density in the real line

Csörnyei, Marianna; Grahl, Jack and O'Neil, Toby C. (2012). Points of middle density in the real line. Real Analysis Exchange, 37(2) pp. 243–248.

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Abstract

A Lebesgue measurable set in the real line has Lebesgue density 0 or 1 at almost every point. Kolyada showed that there is a positive constant $\delta$ such that for non-trivial measurable sets there is at least one point with upper and lower densities lying in the interval $(\delta, 1-\delta)$. Both Kolyada and later Szenes gave bounds for the largest possible value of this $\delta$. In this note we reduce the best known upper bound, disproving a conjecture of Szenes.

Item Type: Journal Article
Copyright Holders: 2012 Michigan State University Press
ISSN: 0147-1937
Keywords: Lebesgue upper density; Lebesgue lower density
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Mathematics, Computing and Technology
Related URLs:
Item ID: 31519
Depositing User: Toby O'Neil
Date Deposited: 29 Nov 2012 10:13
Last Modified: 24 Feb 2016 06:20
URI: http://oro.open.ac.uk/id/eprint/31519
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