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A general duality theorem for marginal problems
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  • Published: September 1995

A general duality theorem for marginal problems

  • D. Ramachandran1 &
  • L. Rüschendorf2 

Probability Theory and Related Fields volume 101, pages 311–319 (1995)Cite this article

  • 287 Accesses

  • 27 Citations

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Summary

Given probability spaces (X i ,A i ,P i ),i=1, 2 letM(P 1,P 2) denote the set of all probabilities on the product space with marginalsP 1 andP 2 and leth be a measurable function on (X 1×X 2,A 1 ⊗A 2). In order to determine supfh dP where the supremum is taken overP inM(P 1,P 2), a general duality theorem is proved. Only the perfectness of one of the coordinate spaces is imposed without any further topological or tightness assumptions. An example without any further topological or tightness assumptions. An example is given to show that the assumption of perfectness is essential. Applications to probabilities with given marginals and given supports, stochastic order and probability metrics are included.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, California State University at Sacramento, 6000 J Street, 95819-6051, Sacramento, CA, USA

    D. Ramachandran

  2. Institut für Mathematische Stochastik, Universität Freiburg, Hebelstrasse 27, D-79104, Freiburg, Germany

    L. Rüschendorf

Authors
  1. D. Ramachandran
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  2. L. Rüschendorf
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Ramachandran, D., Rüschendorf, L. A general duality theorem for marginal problems. Probab. Th. Rel. Fields 101, 311–319 (1995). https://doi.org/10.1007/BF01200499

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  • Received: 17 November 1993

  • Revised: 23 August 1994

  • Issue Date: September 1995

  • DOI: https://doi.org/10.1007/BF01200499

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Mathematics Subject Classification (1991)

  • 60A10
  • 28A35
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