The (sub/super)additivity assertion of Choquet

Heinz König ()
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Heinz König: Universität des Saarlandes, Fakultät für Mathematik und Informatik

A chapter in Measure and Integration, 2012, pp 245-271 from Springer

Abstract: Abstract The assertion in question comes from the short final section in Theory of capacities of Choquet (1953/54), in connection with his prototype of the subsequent Choquet integral. The problem was whether and when this operation is additive. Choquet had the much more abstract idea that all functionals in a certain wide class must be subadditive, and similarly for superadditivity. His treatment of this point was more like an outline, and his proof limited to a rather narrow special case. Thus the proper context and scope of the assertion has remained open. In this paper we present a counterexample which shows that the initial context has to be modified, and then in a new context we prove a comprehensive theorem which fulfils all the needs that have turned up so far.

Keywords: (sub/super)modular and (sub/super)additive functionals; convex functions; Choquet integral; Stonean function classes; Stonean and truncable functionals; Daniell–Stone and Riesz representation theorems (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0382-3_12

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DOI: 10.1007/978-3-0348-0382-3_12

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