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Lower density operators. Φf versus Φd

Ivanova Gertruda, Wagner-Bojakowska Elżbieta, Wilczyński Władysław

Opuscula Mathematica

2023

Vol. 43, no. 2

185--197

Using the new method of the construction of lower density operator introduced in the earlier paper of the first two authors, we study how much the new operator can be different from the classical one. The aim of this paper is to show that if f is a good adjusted measure-preserving bijection then the lower density operator generated by f can be really different from the classical density operator.

Remarks on the topologies in the Lebesgue measurable sets

Hejduk J., Loranty A.

Demonstratio Mathematica

2012

Vol. 45, nr 3

655-663

This paper deals with the abstract density topologies in the family of Lebesgue measurable sets generated by an operator similar to the density lower operator defined in the family of measurable sets.