A Duality-Based Proof of the Triangle Inequality for the Wasserstein Distances

François Golse

doi:10.1007/s44007-023-00082-x

A Duality-Based Proof of the Triangle Inequality for the Wasserstein Distances

François Golse

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Résumé

This short note gives a proof of the triangle inequality based on the Kantorovich duality formula for the Wasserstein distances of exponent p∈[1,+∞) in the case of a general Polish space. In particular, it avoids the “gluing of couplings” procedure used in most textbooks on optimal transport.

langue originale	Anglais
Pages (de - à)	196-210
Nombre de pages	15
journal	Matematica
Volume	3
Numéro de publication	1
Les DOIs	https://doi.org/10.1007/s44007-023-00082-x
état	Publié - 1 mars 2024

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10.1007/s44007-023-00082-x

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abstract = "This short note gives a proof of the triangle inequality based on the Kantorovich duality formula for the Wasserstein distances of exponent p∈[1,+∞) in the case of a general Polish space. In particular, it avoids the “gluing of couplings” procedure used in most textbooks on optimal transport.",

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A Duality-Based Proof of the Triangle Inequality for the Wasserstein Distances

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