A Duality-Based Proof of the Triangle Inequality for the Wasserstein Distances
Optimization and Control
2023-08-08 v1 Metric Geometry
Abstract
This short note gives a proof of the triangle inequality based on the Kantorovich duality formula for the Wasserstein distances of exponent in the case of a general Polish space. In particular it avoids the "glueing of couplings" procedure used in most textbooks on optimal transport.
Keywords
Cite
@article{arxiv.2308.03133,
title = {A Duality-Based Proof of the Triangle Inequality for the Wasserstein Distances},
author = {François Golse},
journal= {arXiv preprint arXiv:2308.03133},
year = {2023}
}
Comments
10 pages, no figure