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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.

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Authors and Affiliations

  1. Dipartimento di Matematica, Informatica ed Economia, Università della Basilicata, Viale dell’Ateneo Lucano, 10, 85100, Potenza, Italy

    Anna Avallone

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  1. Anna Avallone
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Correspondence to Anna Avallone.

Additional information

Communicated by P.De Lucia.

Dedicated to prof. Hans Weber with eternal esteem and gratitude.

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Avallone, A. An Aumann–Shapley type operator in Pseudo-D-lattices. Ricerche mat 67, 413–432 (2018). https://doi.org/10.1007/s11587-018-0383-y

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  • DOI: https://doi.org/10.1007/s11587-018-0383-y

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