On the continuity of correspondences on sets of measures with restricted marginals |
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Authors: | James Bergin |
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Institution: | (1) Department of Economics, Queen's University, Kingston, Ontario, K7L 3N6, CANADA (e-mail: berginj@qed.econ.queensu.ca), CA |
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Abstract: | Summary. Consider the set of probability measures on a product space with the property that all have the same marginal distributions
on the coordinate spaces. This set may be viewed as a correspondence, when the marginal distributions are varied. Here, it
is shown that this correspondence is continuous. Numerous problems in economics involve optimization over a space of measures
where one or more marginal distributions is given. Thus, for this class of problem, Berge's theorem of the maximum is applicable:
the set of optimizers is upper-hemicontinuous and the value of the optimal solution varies with the parameters (marginals)
continuously.
Received: April 23, 1997; revised version: January 16, 1998 |
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Keywords: | and Phrases: Measures on product spaces with restricted marginals Continuity of correspondences on spaces of measures |
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