English

Density Measures

Analysis of PDEs 2026-03-26 v1 Optimization and Control

Abstract

The paper treats density measures as typical examples of finitely additive measures in Rn\mathbb{R}^n. We study their structure and derive basic properties. In addition, estimates for related integrals are provided. The results are applied to the precise representative of general integrable functions and then they are specialized to functions of bounded variation. Moreover, a new representation of the generalized gradients in the sense of Clarke is given for the finite dimensional case.

Keywords

Cite

@article{arxiv.2603.24163,
  title  = {Density Measures},
  author = {Moritz Schönherr and Friedemann Schuricht},
  journal= {arXiv preprint arXiv:2603.24163},
  year   = {2026}
}