CONTENTS§0. Introduction...................................................................................................................................5§1. Notation and terminology..............................................................................................................6§2. A generalization of the Kantorovich-Rubinstein theorem..............................................................8§3. Application: explicit representations for a class of probability metrics.........................................14§4. Topology of the Kantorovich-Rubinstein norm............................................................................18§5. Dual representation for the Wasserstein functional....................................................................21§6. Comparison of Wasserstein functional and Kantorovich-Rubinstein norm; completeness..........27§7. Convergence of empirical measures; results of Fortet-Mourier type..........................................30§8. The convex set of optimal measures..........................................................................................32References......................................................................................................................................34
@book{bwmeta1.element.zamlynska-96c9f8aa-610a-48db-94a1-2c0f49ba2f19,
author = {S. T. Rachev and R. M.},
title = {Duality theorems for Kantorovich-Rubinstein and Wasserstein functionals},
series = {GDML\_Books},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
address = {Warszawa},
year = {1990},
zbl = {0716.60005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-96c9f8aa-610a-48db-94a1-2c0f49ba2f19}
}
S. T. Rachev; R. M. Duality theorems for Kantorovich-Rubinstein and Wasserstein functionals. GDML_Books (1990), http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-96c9f8aa-610a-48db-94a1-2c0f49ba2f19/