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On the extremality, uniqueness and optimality of transference plans. (English) Zbl 1207.90015
For problems in optimal mass transportation theory, the following properties are examined: i) extremality/optimality of the transference plan, ii) uniqueness of the transference plan. Here, the property is used that the problem has a hidden structure of linear preorder with universally measurable graph. Furthermore, the disintegration theorem for measures in countably generated \(\sigma\)-algebras w.r.t. a family of equivalence relations, the construction of optimal potentials, and cyclic and acyclic perturbations are studied. Some examples are given.

90B06 Transportation, logistics and supply chain management