Exceptional points for Lebesgue's density theorem on the real line

Details Exceptional points for Lebesgue's density theorem on the real line Exceptional points for Lebesgue's density theorem on the real line

2007-02-14

arxiv.org/abs/math/0702432v1

Mathematics

Classical Analysis and ODEs

Latex, 11 pages

Scientific paper

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.

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