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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t.c.oneil@open.ac.ukCreated:22 January 2009
Modified:9 November 2012