On the Monotonicity of Optimal Transport
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J.A. Cuesta-Albertos; C. MatrΓ‘n; A. Tuero-DΔ±Μaz
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Article
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1997
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Elsevier Science
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English
β 196 KB
We obtain analytical properties of the maps that give optimal transportation plans for the L 2 -Wasserstein distance. We take advantage of the monotonicity of such optimal transportation plans to discuss their measurability and continuity. As Ε½ a main result of independent interest we obtain the a.e