Generalized Densities on ℝ n and their Applications

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...

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Bibliographic Details
Published inTatra Mountains Mathematical Publications Vol. 78; no. 1; pp. 25 - 42
Main Authors Filipczak, Małgorzata, Terepeta, Małgorzata
Format Journal Article
LanguageEnglish
Published 01.01.2022
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Summary: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.
ISSN:1338-9750
1338-9750
DOI:10.2478/tmmp-2021-0003