Generalized Densities on ℝn and their Applications

Filipczak, Małgorzata; Terepeta, Małgorzata

doi:10.2478/tmmp-2021-0003

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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Generalized Densities on ℝn and their Applications

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