Generalized Densities on ℝ<sup> <i>n</i> </sup> and their Applications-Reference-Cited by-同舟云学术

Generalized Densities on ℝⁿ and their Applications

Published:2021-10-01 Issue:1 Volume:78 Page:25-42
ISSN:1338-9750
Container-title:Tatra Mountains Mathematical Publications
language:en
Short-container-title:

Author:

Filipczak Małgorzata¹,Terepeta Małgorzata²³

Affiliation:

1. 1 Faculty of Mathematics and Computer Science , University of Lodz , Łódź , POLAND

2. 2 Center of Mathematics and Physics Lodz University of Technology , Łódź , POLAND

3. 3 Institute of Mathematics Lodz University of Technology , Łódź , POLAND

Abstract

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.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/tmmp-2021-0003

Reference20 articles.

1. [1] AMBROSIO, L.—FUSCO, N.—PALLARA, D.: Functions of Bounded Variation and Free Discontinuity Problems, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press: New York, 2000.

2. [2] BARTOSZEWICZ, A.—FILIPCZAK, M.—KOWALSKI, A.—TEREPETA, M.: Similarity between topologies, CEJM 12 (2014), no. 4, 603–610.

3. [3] BESICOVITCH, A. S.: A general form of the covering principle and relative differentiation of additive functions, Proc. Cambridge Philos. Soc. 41 (1945), 103–110. A general form of the covering principle and relative differentiation of additive Part II, Proc. Cambridge Philos. Soc. 42 (1946), 1–10.10.1017/S0305004100022660

4. [4] DELLADIO, S.: Functions of class C1 subject to a Legendre condition in an enhanced density set, Rev. Mat. Iberoam. 28 (2012), no. 1, 127–140.

5. [5] DELLADIO, S.: A note on some topological properties of sets with finite perimeter, Glasgow Math. J. 58 (2015), no. 3, 637–647.