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Duality and perfect probability spaces |
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| Authors: | D. Ramachandran L. Rü schendorf |
| Affiliation: | Department Of Mathematics and Statistics, California State University, 6000 J Street, Sacramento, California 95819-6051 ; California State University, Sacramento and Universität Freiburg |
| 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-Rubinv{s}tein (1958) for the case of compact metric spaces are concerned with the validity of the duality
(where |
| Keywords: | Duality theorem marginals perfect measure Marczewski function |
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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.