A Duality-Based Proof of the Triangle Inequality for the Wasserstein Distances
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 "glueing of couplings" procedure used in most textbooks on optimal transport.
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