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The (sub/super)additivity assertion of Choquet
URN: urn:nbn:de:bsz:291-scidok-44192
URL: http://scidok.sulb.uni-saarland.de/volltexte/2011/4419/
pdf-Format:
Dokument 1.pdf (275 KB)
Institut:
Fachrichtung 6.1 - Mathematik
DDC-Sachgruppe:
Mathematik
Dokumentart:
Preprint (Vorabdruck)
Schriftenreihe:
Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Bandnummer:
84
Sprache:
Englisch
Erstellungsjahr:
2003
Publikationsdatum:
06.12.2011
Kurzfassung auf Englisch:
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.
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