Integral representation of continuous comonotonically additive functionals
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- by Lin Zhou PDF
- Trans. Amer. Math. Soc. 350 (1998), 1811-1822 Request permission
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.References
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Additional Information
- Lin Zhou
- Affiliation: Department of Economics, Duke University, Box 90097, Durham, North Carolina 27708-0097
- Email: linzhou@econ.duke.edu
- 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
- © Copyright 1998 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 350 (1998), 1811-1822
- MSC (1991): Primary 28A12, 28C05, 28C15; Secondary 60A05, 60A15, 90A05
- DOI: https://doi.org/10.1090/S0002-9947-98-01735-8
- MathSciNet review: 1373649