
Journal of Convex Analysis 26 (2019), No. 4, 10531058 Copyright Heldermann Verlag 2019 On the Riesz Integral Representation of Additive SetValued Maps (II) Anaté K. Lakmon Department of Mathematics, Faculty of Sciences, University of Lomé, Togo davidlakmon@gmail.com Kazimierz Musial Institute of Mathematics, Wroclaw University, Pl. Grunwaldzki 2/4, 50384 Wroclaw, Poland kazimierz.musial@math.uni.wroc.pl Let T be a compact topological space, and let C_{+}(T) be the space of all nonnegative continuous realvalued functions defined on T endowed with the topology of uniform convergence. We prove the Riesz integral representation for continuous additive and positive setvalued maps defined on C_{+}(T) with values in the space cc(E) of all weakly compact convex nonempty subsets of a Banach space E. As an application we give a generalization of DunfordSchwartz's result on the Riesz integral representation for any continuous setvalued map (not necessary positive). Keywords: Linear maps, setvalued maps, setvalued measures, topology. MSC: 28B20; 54C60 [ Fulltextpdf (85 KB)] for subscribers only. 