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.

DOI: https://doi.org/10.14321/realanalexch.37.2.0243

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.

Viewing alternatives

Metrics

Item Actions

Export

You can export this page using these formats Digital Object Identifier - DOI