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On the characterization of certain similarly ordered super-additive functionals
Author(s):
Heinz
J.
Skala
Journal:
Proc. Amer. Math. Soc.
126
(1998),
1349-1353.
MSC (1991):
Primary 28C05;
Secondary 47H07, 60A05, 90A05
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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:
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
Copyright of article:
Copyright
1998,
American Mathematical Society
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