Density Measures
Moritz Sch\"onherr, Friedemann Schuricht
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Abstract
The paper treats density measures as typical examples of finitely additive measures in . 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.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Point processes and geometric inequalities · Advanced Harmonic Analysis Research