Exceptional points for Lebesgue's density theorem on the real line
Classical Analysis and ODEs
2007-05-23 v1 Combinatorics
Abstract
For a nontrivial measurable set on the real line, there are always exceptional points, where the lower and upper densities of the set are neither zero nor one. We quantify this statement, following work by V. Kolyada, and obtain the unexpected result that there is always a point where the upper and the lower densities are closer to 1/2 than to zero or one. The method of proof uses a combinatorial restatement of the problem.
Cite
@article{arxiv.math/0702432,
title = {Exceptional points for Lebesgue's density theorem on the real line},
author = {Andras Szenes},
journal= {arXiv preprint arXiv:math/0702432},
year = {2007}
}
Comments
Latex, 11 pages