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 on the closed subspace of BV generated by powers of nonatomic σ-additive positive modular measures on L. The integral representation of on a class of functions that correspond to measure games is also exhibited.
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Dedicated to Professor Paolo De Lucia on the occasion of his 70th birthday.
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Avallone, A., Basile, A. & Vitolo, P. Positive Operators à la Aumann-Shapley on Spaces of Functions on D-Lattices. Positivity 10, 701–719 (2006). https://doi.org/10.1007/s11117-006-0052-3
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DOI: https://doi.org/10.1007/s11117-006-0052-3