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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Integral representation of continuous
comonotonically additive functionals

Author: Lin Zhou
Journal: Trans. Amer. Math. Soc. 350 (1998), 1811-1822
MSC (1991): Primary 28A12, 28C05, 28C15; Secondary 60A05, 60A15, 90A05
MathSciNet review: 1373649
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Abstract: In this paper, I first prove an integral representation theorem: Every quasi-integral on a Stone lattice can be represented by a unique upper-continuous capacity. I then apply this representation theorem to study the topological structure of the space of all upper-continuous capacities on a compact space, and to prove the existence of an upper-continuous capacity on the product space of infinitely many compact Hausdorff spaces with a collection of consistent finite marginals.

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Additional Information

Lin Zhou
Affiliation: Department of Economics, Duke University, Box 90097, Durham, North Carolina 27708-0097

Keywords: Upper-continuous capacities, regular capacities, Choquet integrals, Stone lattices, comonotonically additive functionals, monotonic functionals, continuous functionals, the weak topology, Kolmogorov's theorem, consistent marginals
Received by editor(s): August 16, 1995
Received by editor(s) in revised form: October 30, 1995
Additional Notes: I want to thank L. Epstein, D. Schmeidler, and in particular, M. Marinacci, as well as an anonymous referee, for their helpful comments. The revision was done while I was visiting the Economics Department of the Hong Kong University of Science and Technology, whose hospitality I deeply appreciated
Article copyright: © Copyright 1998 American Mathematical Society