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arXiv · 2606.19385

On the family of measurable sets having the upper positive density

Jacek Hejduk·Renata Wiertelak·Władysław Wilczyński
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Abstract

The essence of the density topology lies in the family of Lebesgue measurable sets where each point of a set is a density point of that set. The motivation of this work is to investigate the family of measurable sets for which, at every point within a set belonging to this family, the upper density of that set is positive. We obtain a strong generalized topology, and its essential properties are demonstrated in comparison with those of the classical density topology.

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Jacek Hejduk, Renata Wiertelak, Władysław Wilczyński. 2026-06-15. On the family of measurable sets having the upper positive density. https://arxiv.org/abs/2606.19385

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