An Aumann–Shapley type operator in Pseudo-D-lattices

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Abstract

Let L be a \(\sigma \)-complete pseudo-D-lattice and let BV be the Banach space of all real-valued, vanishing at zero, functions of bounded variation on L endowed with the variation norm. We prove the existence of a continuous Aumann–Shapley type operator \(\phi \) on the closed subspace of BV spanned by powers of nonatomic \(\sigma \)-additive positive modular measures on L. Moreover we give an integral representation of \(\phi \) on a class of functions that correspond to measure games.

Keywords

Pseudo-D-lattices Measures Aumann–Shapley operator Measure games 

Mathematics Subject Classification

28A12 06C15 91A12 

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Copyright information

© Università degli Studi di Napoli "Federico II" 2018

Authors and Affiliations

  1. 1.Dipartimento di Matematica, Informatica ed EconomiaUniversità della BasilicataPotenzaItaly

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