Journal of Convex Analysis 29 (2022), No. 4, 1119--1148
Copyright Heldermann Verlag 2022
Representations of Multimeasures via the Multivalued Bartle-Dunford-Schwartz 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 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 dH-multimeasures; equivalent conditions are provided in both cases.
Keywords: Locally convex space, multifunction, Bartle-Dunford-Schwartz integral, support function, selection, Radon-Nikodym theorem.
MSC: 28B20; 26E25, 26A39, 28B05, 46G10, 54C60, 54C65.
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