An elementary proof of the triangle inequality for the Wasserstein metric |
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| Authors: | Philippe Clement Wolfgang Desch |
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| Affiliation: | Mathematical Institute, Leiden University, P. O. Box 9512, NL-2300 RA Leiden, The Netherlands ; Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universität Graz, Heinrichstrasse 36, 8010 Graz, Austria |
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| Abstract: | ![]()
We give an elementary proof for the triangle inequality of the  -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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| Keywords: | Wasserstein metric triangle inequality probability measures on metric spaces |
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