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Wasserstein Distance

  • Szymon M. Walczak
Chapter
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Abstract

The Wasserstein distance of Borel probability measures will play the important role in metric diffusion along foliations. We here present the Kantorovich Duality Theorem for optimal transportation problem. We also recall the definition of the Wasserstein distance, together with the weak-∗ topology metrization theorem for the set \(\mathscr{P}(X)\) of Borel probability measures on a compact metric space X. The chapter is closed by some technical lemmas used in the later considerations.

Keywords

Transportation Cost Full Generality Technical Lemma Borel Probability Measure Transportation Plan 
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References

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    Villani, C.: Optimal Transport, Old and New. Grundlehren der mathematischen Wissenschaften, vol. 338. Springer, New York (2009)Google Scholar
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    Villani, C.: Topics in Optimal Transportation. American Mathematical Society, Providence (2003)CrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Szymon M. Walczak
    • 1
    • 2
  1. 1.National Science CenterKrakówPoland
  2. 2.Faculty of Mathematics and Computer ScienceUniversity of ŁódźŁódźPoland

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