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The (sub/super)additivity assertion of Choquet

In: Measure and Integration

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  • Heinz König

    (Universität des Saarlandes, Fakultät für Mathematik und Informatik)

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.

Suggested Citation

  • Heinz König, 2012. "The (sub/super)additivity assertion of Choquet," Springer Books, in: Measure and Integration, edition 127, pages 245-271, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-0382-3_12
    DOI: 10.1007/978-3-0348-0382-3_12
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