Optimal quality of exceptional points for the Lebesgue density theorem

Details Optimal quality of exceptional points for the Lebesgue density theorem Optimal quality of exceptional points for the Lebesgue density theorem

2011-05-23

arxiv.org/abs/1105.4634v1

Mathematics

Classical Analysis and ODEs

45 pages

Scientific paper

In spite of the Lebesgue density theorem, there is a positive $\delta$ such that, for every non-trivial measurable set $S$ of real numbers, there is a point at which both the lower densities of $S$ and of the complement of $S$ are at least $\delta$. The problem of determining the supremum of possible values of this $\delta$ was studied in a paper of V. I. Kolyada, as well as in some recent papers. We solve this problem in the present work.

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