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:	Article
Copyright Holders:	2012 Michigan State University Press
ISSN:	0147-1937
Keywords:	Lebesgue upper density; Lebesgue lower density
Academic Unit/School:	Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM)
Related URLs:	http://msupress.msu.edu/journals/raex/in...(Other)
Item ID:	31519
Depositing User:	Toby O'Neil
Date Deposited:	29 Nov 2012 10:13
Last Modified:	06 Oct 2016 00:19
URI:	http://oro.open.ac.uk/id/eprint/31519
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