Points of middle density in the real line.

Marianna Csörnyei, Jack Grahl and Toby C O'Neil

Published in Real Analysis Exchange 37(2) (2012) 243-248.


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.

A postscript and pdf files of the preprint are available.

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Created:22 January 2009
Modified:9 November 2012