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Generalized Densities on ℝn and their Applications

Małgorzata Filipczak

Małgorzata Filipczak

Faculty of Mathematics and Computer Science, University of LodzŁódź, POLAND
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Filipczak, Małgorzata
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Małgorzata Terepeta

Małgorzata Terepeta

  • Center of Mathematics and Physics Lodz University of TechnologyŁódź, POLAND
  • Institute of Mathematics Lodz University of TechnologyŁódź, POLAND
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Terepeta, Małgorzata
  
Jan 01, 2022
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Published Online: Jan 01, 2022
Page range: 25 - 42
Received: Oct 12, 2020
DOI: https://doi.org/10.2478/tmmp-2021-0003
Keywords
© 2021 Mathematical Institute, Slovak Academy of Sciences
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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.

Language:
English
Publication timeframe:
3 times per year
Journal Subjects:
Mathematics, General Mathematics
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