2019•Functional Analysis and Its ApplicationsRequires access

Densities of Measures as an Alternative to Derivatives for Measurable Inclusions

Alexander Alexandrovich Tolstonogov

Abstract

Rules for calculating the densities of Borel measures which are absolutely continuous with respect to a positive nonatomic Radon measure are considered. The Borel measures are generated by composite functions which depend on continuous functions of bounded variation defined on an interval. Questions related to the absolute continuity of Borel measures generated by composite functions with respect to a positive Radon measure and rules for calculating the densities of Borel measures generated by composite functions with respect to a positive nonatomic Radon measure are studied.

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Key concepts: Mathematics, Borel measure, Absolute continuity, Measurable function, Measure (data warehouse), Radon measure, Bounded function, Borel set