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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

Kazimierz Musial
Institut of Mathematics, Wroclaw University, Poland

Anna Rita Sambucini
Dept. of Mathematics and Computer Sciences, University of Perugia, Italy

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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