Duality and perfect probability spaces
Authors:
D. Ramachandran and L. Rüschendorf
Journal:
Proc. Amer. Math. Soc. 124 (1996), 22232228
MSC (1991):
Primary 60A10, 28A35
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 KantorovichRubin\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 958196051
Email:
chandra@csus.edu
L. Rüschendorf
Affiliation:
California State University, Sacramento and Universität Freiburg
Address at time of publication:
Institut für Mathematische Stochastik, AlbertLudwigsUniversität, Hebelstr. 27, D79104 Freiburg, Germany
Email:
ruschen@buffon.mathematik.unifreiburg.de
DOI:
http://dx.doi.org/10.1090/S0002993996034624
PII:
S 00029939(96)034624
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
