Journal of Convex Analysis 26 (2019), No. 4, 1053--1058
Copyright Heldermann Verlag 2019
On the Riesz Integral Representation of Additive Set-Valued Maps (II)
Anaté K. Lakmon
Department of Mathematics, Faculty of Sciences, University of Lomé, Togo
Institute of Mathematics, Wroclaw University, Pl. Grunwaldzki 2/4, 50-384 Wroclaw, Poland
Let T be a compact topological space, and let C+(T) be the space of all non-negative continuous real-valued functions defined on T endowed with the topology of uniform convergence. We prove the Riesz integral representation for continuous additive and positive set-valued maps defined on C+(T) with values in the space cc(E) of all weakly compact convex non-empty subsets of a Banach space E. As an application we give a generalization of Dunford-Schwartz's result on the Riesz integral representation for any continuous set-valued map (not necessary positive).
Keywords: Linear maps, set-valued maps, set-valued measures, topology.
MSC: 28B20; 54C60
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