# Points of middle density in the real line.

## 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 $$\delta$$ 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.