On the continuity of correspondences on sets of measures with restricted marginals

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)471-481
Journal / PublicationEconomic Theory
Issue number2
Publication statusPublished - Feb 1999
Externally publishedYes


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.

Research Area(s)

  • Continuity of correspondences on spaces of measures, Measures on product spaces with restricted marginals