Optimal maps for the multidimensional Mo
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Wilfrid Gangbo; Andrzej Święch
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Article
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1998
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John Wiley and Sons
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English
⚖ 261 KB
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