A Duality-Based Proof of the Triangle Inequality for the Wasserstein Distances
La Matematica(2024)
摘要
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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关键词
Wasserstein distance,Kantorovich duality,Triangle inequality,Optimal transport,49Q22,49N15 (60B10)
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