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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An elementary proof of the triangle inequality for the Wasserstein metric
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by Philippe Clement and Wolfgang Desch PDF
Proc. Amer. Math. Soc. 136 (2008), 333-339 Request permission


We give an elementary proof for the triangle inequality of the $p$-Wasserstein metric for probability measures on separable metric spaces. Unlike known approaches, our proof does not rely on the disintegration theorem in its full generality; therefore the additional assumption that the underlying space is Radon can be omitted. We also supply a proof, not depending on disintegration, that the Wasserstein metric is complete on Polish spaces.
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Additional Information
  • Philippe Clement
  • Affiliation: Mathematical Institute, Leiden University, P. O. Box 9512, NL-2300 RA Leiden, The Netherlands
  • Email:
  • Wolfgang Desch
  • Affiliation: Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universität Graz, Heinrichstrasse 36, 8010 Graz, Austria
  • Email:
  • Received by editor(s): October 30, 2006
  • Published electronically: September 27, 2007
  • Communicated by: Richard C. Bradley
  • © Copyright 2007 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 333-339
  • MSC (2000): Primary 60B05
  • DOI:
  • MathSciNet review: 2350420