Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

An elementary proof of the triangle inequality for the Wasserstein metric
HTML articles powered by AMS MathViewer

by Philippe Clement and Wolfgang Desch PDF
Proc. Amer. Math. Soc. 136 (2008), 333-339 Request permission

Abstract:

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.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 60B05
  • Retrieve articles in all journals with MSC (2000): 60B05
Additional Information
  • Philippe Clement
  • Affiliation: Mathematical Institute, Leiden University, P. O. Box 9512, NL-2300 RA Leiden, The Netherlands
  • Email: philippeclem@gmail.com
  • Wolfgang Desch
  • Affiliation: Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universität Graz, Heinrichstrasse 36, 8010 Graz, Austria
  • Email: georg.desch@uni-graz.at
  • 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: https://doi.org/10.1090/S0002-9939-07-09020-X
  • MathSciNet review: 2350420