# 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 such that for non-trivial measurable sets there is at least one point with upper and lower densities lying in the interval . Both Kolyada and later Szenes gave bounds for the largest possible value of this . In this note we reduce the best known upper bound, disproving a conjecture of Szenes.

Item Type: Journal Article 2012 Michigan State University Press 0147-1937 Lebesgue upper density; Lebesgue lower density Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and StatisticsFaculty of Science, Technology, Engineering and Mathematics (STEM) http://msupress.msu.edu/journals/raex/in...(Other) 31519 Toby O'Neil 29 Nov 2012 10:13 04 Aug 2016 15:21 http://oro.open.ac.uk/id/eprint/31519
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