Please use this identifier to cite or link to this item: doi:10.22028/D291-26236
Title: The (sub/super)additivity assertion of Choquet
Author(s): König, Heinz
Language: English
Year of Publication: 2003
DDC notations: 510 Mathematics
Publikation type: Preprint
Abstract: The assertion in question comes from the short final section in the Theory of Capacities of Choquet 1953/54, in connection with his prototype of the subsequent Choquet integral. The problem was whether and when this formation is additive. Choquet had the much more abstract idea that all functionals in a certain wide class must be subadditive, and the counterpart with superadditive. His treatment of this point was kind of an outline, and his proof limited to a rather narrow special case. Thus the adequate context and scope of the assertion remained open even up to now. In this paper we present a counterexample which shows that the initial context has to be modified, and then in new context a comprehensive theorem which fulfils all needs turned up so far.
Link to this record: urn:nbn:de:bsz:291-scidok-44192
hdl:20.500.11880/26292
http://dx.doi.org/10.22028/D291-26236
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 84
Date of registration: 6-Dec-2011
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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