A characterization for the solution of the Monge--Kantorovich mass transference problem

J. A. Cuesta-Albertos and A. Tuero-Díaz

Statistics & Probability Letters, 1993, vol. 16, issue 2, 147-152

Abstract: Let P and Q be probabilities on the Borel [sigma]-algebra in a metric space (M, d). We prove that if the support of Q is finite and P verifies a certain continuity condition, then all the solutions of the Monge-Kantorovich mass transference problem between P and Q can be written as (X, H(X)) where X is any random element with distribution P and H only depends on P and Q.

Keywords: Monge-Kantorovich; mass; transference; problem; Wasserstein; distances; Mallows; distances; unicity; metric; spaces (search for similar items in EconPapers)
Date: 1993
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