Abstract
In spite of the Lebesgue density theorem, there is a positive such that, for every measurable set with and , there is a point at which both the lower densities of and of the complement of A are at least . The problem of determining the supremum of possible values of this was studied by V. I. Kolyada, A. Szenes and others, and it was solved by O. Kurka. Lower density of at is defined as a lower limit of . Replacing by for a fixed decreasing sequence tending to zero, we obtain a definition of the constant . In our paper we look for an upper bound of all such constants.
Citation
Tomasz Filipczak. Grażyna Horbaczewska. "EXCEPTIONAL POINTS FOR DENSITIES GENERATED BY SEQUENCES." Real Anal. Exchange 46 (2) 305 - 317, 2021. https://doi.org/10.14321/realanalexch.46.2.0305
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