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Optimal maps for the multidimensional Monge-Kantorovich problem

✍ Scribed by Wilfrid Gangbo; Andrzej Święch

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
261 KB
Volume
51
Category
Article
ISSN
0010-3640

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✦ Synopsis

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 problem investigated in this paper consists of finding S = (S1, . . . , SN ) ∈ Γ(µ1, . . . , µN ) minimizing I[T

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A General Solution of the Monge–Kantorov
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