Representations of Multimeasures via the Multivalued Bartle-Dunford-Schwartz Integral

An integral for a scalar function with respect to a multimeasure N taking its values in a locally convex space is introduced. The definition is independent of the selections of N and is related to a functional version of the Bartle-Dunford-Schwartz integral with respect to a vector measure presented by Lewis. Its properties are studied together with its application to Radon-Nikodym theorems in order to represent as an integrable derivative the ratio of two general multimeasures or two $d_H$-multimeasures; equivalent conditions are provided in both cases.