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A variational proof of Aumann's theorem

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Abstract

We give a new proof of Aumann's theorem on the integrals of multifunctions. The proof, which is variational in nature, also leads to a constructive procedure for calculating a selection whose integral approximates a given point in the integral of the multifunction.

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Authors and Affiliations

  1. Department of Mathematics, University of British Columbia, V6T 1Y4, Vancouver, B.C., Canada

    Frank H. Clarke

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  1. Frank H. Clarke
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Additional information

Communicated by A. Bensoussan

The support of the Natural Sciences and Engineering Research Council of Canada (grant A 9082) and of the Killam Foundation (Canada Council Senior Research Fellowship) is gratefully acknowledged.

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Clarke, F.H. A variational proof of Aumann's theorem. Appl Math Optim 7, 373–378 (1981). https://doi.org/10.1007/BF01442127

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  • DOI: https://doi.org/10.1007/BF01442127

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