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Scientific article
English

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

ContributorsSzenes, Andras
Published inAdvances in mathematics, vol. 226, no. 1, p. 764-778
Publication date2011
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 0 nor 1. 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 discretized restatement of the problem, and a self-similar construction.

Keywords
  • Lebesgue density theorem
  • Measurable sets
  • Fractals
  • Interval configurations
Citation (ISO format)
SZENES, Andras. Exceptional points for Lebesgue’s density theorem on the real line. In: Advances in mathematics, 2011, vol. 226, n° 1, p. 764–778. doi: 10.1016/j.aim.2010.07.011
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Article (Published version)
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Identifiers
ISSN of the journal0001-8708
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