On the Riesz Integral Representation of Additives Set-Valued Maps (I)
Lakmon A. Kodjovi *
Department of Mathematics, University of Lomé, Togo
Siggini K. Kenny
Department of Mathematics, University of Lomé, Togo
Ayassou Emmanuel
Department of Mathematics, University of Lomé, Togo
Tchari`e Kokou
Department of Mathematics, University of Lomé, Togo
*Author to whom correspondence should be addressed.
Abstract
In this paper we generalize the Riesz integral representation for continuous linear maps associated with additive set-valued maps with values in the set of all closed bounded convex non-empty subsets of any Banach space. We deduce the Riesz integral representation results for set-valued maps, for vector-valued maps of Diestel-Uhl and for scalar-valued maps of Dunford-Schwartz.
Keywords: Linear maps associated with additive set-valued maps, set-valued measures, integral representation; topology