On the continuity of correspondences on sets of measures with restricted marginals
- Cite this article as:
- Bergin, J. Economic Theory (1999) 13: 471. doi:10.1007/s001990050265
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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.