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Remarks on Afriat’s theorem and the Monge–Kantorovich problem

✍ Scribed by Kolesnikov, Alexander V.; Kudryavtseva, Olga V.; Nagapetyan, Tigran


Book ID
120623452
Publisher
Elsevier Science
Year
2013
Tongue
English
Weight
257 KB
Volume
49
Category
Article
ISSN
0304-4068

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Optimal maps for the multidimensional Mo
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Let µ1, . . . , µN be Borel probability measures on R d . Denote by Γ(µ1, . . . , µN ) the set of all N -tuples T = (T1, . . . , TN ) such that Ti : R d → R d (i = 1, . . . , N) are Borel-measurable and satisfy µ1[T -1 i (V )] = µi[V ] for all Borel V ⊂ R d . The multidimensional Monge-Kantorovich p