Optimal quality of exceptional points for the Lebesgue density theorem
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- 作者：Ond艡ej Kurka (1) kurka.ondrej@seznam.cz
- 关键词：Key words and phrases Lebesgue density theorem – ; exceptional point – ; interval configuration
- 刊名：Acta Mathematica Hungarica
- 出版时间：February 2012
- 出版年：2012
- 期刊代码：2_02365294
- 类别：ch
- 卷：134
- 期：3
- 页码：209-268
- 数据来源：sp
摘要
In spite of the Lebesgue density theorem, there is a positive δ such that, for every non-trivial measurable set S⊂ℝ, there is a point at which both the lower densities of S and of ℝ∖S are at least δ. The problem of determining the supremum of possible values of this δ was studied in a paper of V. I. Kolyada, as well as in some recent papers. We solve this problem in the present work.