Csörnyei, Marianna; Grahl, Jack and O'Neil, Toby C.
Points of middle density in the real line.
Real Analysis Exchange, 37(2) pp. 243–248.
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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.
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