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2011/2012 Points of Middle Density in the Real Line
Marianna Csörnyei, Jack Grahl, Toby C. O'Neil
Real Anal. Exchange 37(2): 243-248 (2011/2012).


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.


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Marianna Csörnyei. Jack Grahl. Toby C. O'Neil. "Points of Middle Density in the Real Line." Real Anal. Exchange 37 (2) 243 - 248, 2011/2012.


Published: 2011/2012
First available in Project Euclid: 15 April 2013

zbMATH: 1276.28009
MathSciNet: MR3080589

Primary: 28A75

Keywords: Lebesgue lower density , Lebesgue upper density

Rights: Copyright © 2011 Michigan State University Press

Vol.37 • No. 2 • 2011/2012
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