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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the characterization of certain
similarly ordered super-additive functionals


Author: Heinz J. Skala
Journal: Proc. Amer. Math. Soc. 126 (1998), 1349-1353
MSC (1991): Primary 28C05; Secondary 47H07, 60A05, 90A05
MathSciNet review: 1476392
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Abstract: Functionals which behave (sub-, super-) additively on similarly ordered functions occur quite naturally in many contexts. In the present paper we characterize (super-) additive functionals which are defined on a family of functions with the Stone-property in terms of their naturally adjoined dyadic martingales. As corollaries we obtain essential generalizations of integral representations as derived by Schmeidler (1986) and discussed in a recent monograph of Denneberg (1994).


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Additional Information

Heinz J. Skala
Affiliation: Department of Statistics, University of Paderborn, Warburgerstrasse 100, 33095 Paderborn, Germany

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04702-9
PII: S 0002-9939(98)04702-9
Keywords: Similarly ordered, comonotonic, integral representation, martingales
Received by editor(s): August 29, 1996
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1998 American Mathematical Society