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

Published in Advances in Mathematics. 2011, vol. 226, no. 1, p. 764-778
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 theoremMeasurable setsFractalsInterval configurations
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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. https://archive-ouverte.unige.ch/unige:16440

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Deposited on : 2011-06-27

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