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Regularity of Potential Functions of the Optimal Transportation Problem

✍ Scribed by Xi-Nan Ma; Neil S. Trudinger; Xu-Jia Wang


Publisher
Springer
Year
2005
Tongue
English
Weight
279 KB
Volume
177
Category
Article
ISSN
0003-9527

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Suppose that P and Q are probabilities on a separable Banach space ~:. It is known that if (P, Q) satisfies certain regularity conditions and a random variable X has law P, then there exists a function f : ~: ~ IF, such that the function f(X) has the law Q and the random pair (X,f(X)) is an optimal