Abstract

Let T be a compact topological space, and let C+(T)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)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).

Author information

Contact details are reproduced from the original publication and may be historical.

Anaté K. Lakmon

Department of Mathematics, Faculty of Sciences, University of Lomé, Togo

davidlakmon@gmail.com

Keywords

  • Linear maps
  • set-valued maps
  • set-valued measures
  • topology

Mathematics Subject Classification

28B20; 54C60

References

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Suggested citation

A. K. Lakmon, K. Musiał. “On the Riesz Integral Representation of Additive Set-Valued Maps (II).” Journal of Convex Analysis 26 (2019), No. 4, 1053–1058. https://doi.org/10.68381/jca26056

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Published by Heldermann Verlag, 2019. Rights now held by Banach Press LLC.