On the Riesz Integral Representation of Additive Set-Valued Maps (II)
JOURNAL OF CONVEX ANALYSIS(2019)
Abstract
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).
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Key words
Linear maps,set-valued maps,set-valued measures,topology
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