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

François Golse

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arXiv · 2308.03133

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

François Golse

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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 $p\in[1,+\infty)$ in the case of a general Polish space. In particular it avoids the "glueing of couplings" procedure used in most textbooks on optimal transport.

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François Golse. 2023-08-06. A Duality-Based Proof of the Triangle Inequality for the Wasserstein Distances. https://arxiv.org/abs/2308.03133

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