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

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dc.creatorSzenes, Andras
dc.date2007-02-14
dc.date.accessioned2026-07-07T07:47:03Z
dc.date.available2026-07-07T07:47:03Z
dc.descriptionFor 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.
dc.descriptionLatex, 11 pages
dc.identifierhttps://arxiv.org/abs/math/0702432
dc.identifierhttp://arxiv.org/abs/math/0702432
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/124037
dc.subjectClassical Analysis and ODEs
dc.subjectCombinatorics
dc.titleExceptional points for Lebesgue's density theorem on the real line
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