
Journal of Convex Analysis 29 (2022), No. 4, 11191148 Copyright Heldermann Verlag 2022 Representations of Multimeasures via the Multivalued BartleDunfordSchwartz Integral Luisa Di Piazza Dept. of Mathematics, University of Palermo, Italy luisa.dipiazza@unipa.it Kazimierz Musial Institut of Mathematics, Wroclaw University, Poland kazimierz.musial@math.uni.wroc.pl Anna Rita Sambucini Dept. of Mathematics and Computer Sciences, University of Perugia, Italy anna.sambucini@unipg.it 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 BartleDunfordSchwartz integral with respect to a vector measure presented by Lewis. Its properties are studied together with its application to RadonNikodym 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. Keywords: Locally convex space, multifunction, BartleDunfordSchwartz integral, support function, selection, RadonNikodym theorem. MSC: 28B20; 26E25, 26A39, 28B05, 46G10, 54C60, 54C65. [ Fulltextpdf (203 KB)] for subscribers only. 