On the characterization of certain similarly ordered super-additive functionals

Skala, Heinz

doi:10.1090/S0002-9939-98-04702-9

On the characterization of certain similarly ordered super-additive functionals
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by Heinz J. Skala

Proc. Amer. Math. Soc. 126 (1998), 1349-1353

DOI: https://doi.org/10.1090/S0002-9939-98-04702-9

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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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