Generalized Densities on ℝn and their Applications

Małgorzata Filipczak; Małgorzata Terepeta

doi:10.2478/tmmp-2021-0003

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Generalized Densities on ℝn and their Applications

Tatra Mountains Mathematical Publications

Volume 78 (2021): Issue 1 (October 2021)

By: Małgorzata Filipczak and Małgorzata Terepeta

Open Access

|Jan 2022

Abstract

We examine some generalized densities (called (ψ, n)-densities) obtained as a result of strengthening the Lebesgue Density Theorem. It turns out that these notions are the generalizations of superdensity, enhanced density and m-density, and have some applications in the theory of sets of finite perimeter and in Sobolev spaces.

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Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2021-0003 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 25 - 42

Submitted on: Oct 12, 2020

Published on: Jan 1, 2022

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

ψ - density point,

ψ - density topology,

similarity of topologies,

differentiation basis,

base operator,

set of finite perimeter,

Sobolev space

Related subjects:

Mathematics,

General mathematics

© 2022 Małgorzata Filipczak, Małgorzata Terepeta, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 78 (2021): Issue 1 (October 2021)