Economic Theory

, Volume 13, Issue 2, pp 471–481

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

  • James Bergin
Exposita Notes

DOI: 10.1007/s001990050265

Cite this article as:
Bergin, J. Economic Theory (1999) 13: 471. doi:10.1007/s001990050265


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.

Keywords and Phrases: Measures on product spaces with restricted marginals Continuity of correspondences on spaces of measures. 
JEL Classification Numbers: C60 C61. 

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • James Bergin
    • 1
  1. 1.Department of Economics, Queen's University, Kingston, Ontario, K7L 3N6, CANADA (e-mail:

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