An Extension of the Kantorovich-Rubinstein Mass-Transshipment Problem

Leonid Hanin, Svetlozar T. Rachev

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


The classical Kantorovich-Rubinstein theorem for mass transshipment is generalized. For Borel measures µ on IRn with zero mixed moments of order less than k, we obtain a dual representation of the norm where гµ, stands for the set of transshipment plans ψ satisfying the balancing condition and is the k-th difference with step h. We show that ||P — Q||r is an “ideal” metric in the space of probabilities on IRn. Applications of generalized Kantorovich metrics in cancer radiotherapy and in collision resolution for multiple-access protocols are discussed.

Original languageEnglish
Pages (from-to)701-735
Number of pages35
JournalNumerical Functional Analysis and Optimization
Issue number5-6
StatePublished - 1995


  • ideal metrics
  • mass-transshipment problem
  • probability metrics


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