The variation of vector measures and cylindrical concentration (Q1067033)

Given a vector measure with values in a locally convex space E absolutely continuous with respect to a scalar measure, the additivity of the associated cylindrical measure on E is closely associated with the differentiability of the vector measure. The paper examines this relationship and shows how the variation of the vector measure is related to the cylindrical concentration on a family of subsets of E, of the associated cylindrical measure. Necessary and sufficient conditions are given for a vector measure with values in a space of signed Radon measures to be differentiable with respect to a scalar measure. The results are used to show that regular densities for a vector measure with respect to a scalar measure are essentially unique.