Let L be a σ-complete D-lattice and BV the AL-space of all realvalued, null in zero, functions on L of bounded variation. We prove the existence of a continuous Aumann-Shapley operator φ on the closed subspace of BV generated by powers of nonatomic σ-additive positive modular measures on L. The integral representation of φ on a class of functions that correspond to measure games is also exhibited.
Positive operators à la Aumann-Shapley on spaces of functions on D-lattices
AVALLONE, Anna;VITOLO, Paolo
2006-01-01
Abstract
Let L be a σ-complete D-lattice and BV the AL-space of all realvalued, null in zero, functions on L of bounded variation. We prove the existence of a continuous Aumann-Shapley operator φ on the closed subspace of BV generated by powers of nonatomic σ-additive positive modular measures on L. The integral representation of φ on a class of functions that correspond to measure games is also exhibited.File in questo prodotto:
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