Duality and perfect probability spaces

Authors:
D. Ramachandran and L. Rüschendorf

Journal:
Proc. Amer. Math. Soc. **124** (1996), 2223-2228

MSC (1991):
Primary 60A10, 28A35

DOI:
https://doi.org/10.1090/S0002-9939-96-03462-4

MathSciNet review:
1342043

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Abstract: Given probability spaces let denote the set of all probabilities on the product space with marginals and and let be a measurable function on Continuous versions of linear programming stemming from the works of Monge (1781) and Kantorovich-Rubin\v{s}tein (1958) for the case of compact metric spaces are concerned with the validity of the duality

(where is the collection of all probability measures on with and as the marginals). A recently established general duality theorem asserts the validity of the above duality whenever at least one of the marginals is a perfect probability space. We pursue the converse direction to examine the interplay between the notions of duality and perfectness and obtain a new characterization of perfect probability spaces.

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Additional Information

**D. Ramachandran**

Affiliation:
Department Of Mathematics and Statistics, California State University, 6000 J Street, Sacramento, California 95819-6051

Email:
chandra@csus.edu

**L. Rüschendorf**

Affiliation:
California State University, Sacramento and Universität Freiburg

Address at time of publication:
Institut für Mathematische Stochastik, Albert-Ludwigs-Universität, Hebelstr. 27, D-79104 Freiburg, Germany

Email:
ruschen@buffon.mathematik.uni-freiburg.de

DOI:
https://doi.org/10.1090/S0002-9939-96-03462-4

Keywords:
Duality theorem,
marginals,
perfect measure,
Marczewski function

Received by editor(s):
December 15, 1994

Additional Notes:
Research supported in part by an Internal Awards Grant from the California State University, Sacramento

Communicated by:
Richard T. Durrett

Article copyright:
© Copyright 1996
American Mathematical Society