Densities of measures as an alternative to derivatives for measurable inclusions

In the paper, we consider rules for calculating the densities of Borel measures which are absolutely continuous with respect to a positive non-atomic Radon measure. The Borel measures are generated by composite functions which depend on continuous functions of bounded variation defined on an interval. The questions of the absolute continuity of Borel measures generated by composite functions with respect to the positive Radon measure and rules for calculating the densities of Borel measures generated by composite functions with respect to the positive non-atomic Radon measure are studied.