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unige:16440 
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Exceptional points for Lebesgue's density theorem on the real line |
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| 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 theorem — Measurable sets — Fractals — Interval configurations | |
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Article (Published version) (155 Kb) - Limited access to UNIGE Other version: http://linkinghub.elsevier.com/retrieve/pii/S0001870810002719 |
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| Structures | ||
| 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. https://archive-ouverte.unige.ch/unige:16440 |
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