<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>We examine some generalized densities (called (<italic>ψ, n</italic>)-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 <italic>m</italic>-density, and have some applications in the theory of sets of finite perimeter and in Sobolev spaces.</p>
</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.

Generalized Densities on ℝ<sup><italic>n</italic></sup> and their Applications

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Generalized Densities on ℝ and their Applications

We examine some generalized densities (called (ψ, n)-densities) obtained as a result of strengthening the Lebesgue Density Theorem. It turns out that these...

Generalized Densities on ℝⁿ and their Applications

Published Online: Jan 01, 2022

Page range: 25 - 42

Received: Oct 12, 2020

DOI: https://doi.org/10.2478/tmmp-2021-0003

Keywords
- density point, - density topology, similarity of topologies, differentiation basis, base operator, set of finite perimeter, Sobolev space

© 2021 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Generalized Densities on ℝn and their Applications

Published Online: Jan 01, 2022

Page range: 25 - 42

Received: Oct 12, 2020

DOI: https://doi.org/10.2478/tmmp-2021-0003

Keywords- density point, - density topology, similarity of topologies, differentiation basis, base operator, set of finite perimeter, Sobolev space

© 2021 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Generalized Densities on ℝⁿ and their Applications

Keywords
- density point, - density topology, similarity of topologies, differentiation basis, base operator, set of finite perimeter, Sobolev space