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A Duality-Based Proof of the Triangle Inequality for the Wasserstein Distances
- Publication Year :
- 2023
-
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.<br />Comment: 10 pages, no figure
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2308.03133
- Document Type :
- Working Paper