Geodesic
Calculation of the Wasserstein distance between probability distributions on the line
Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 4, pp. 824-827

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We prove that the Wasserstein distance between probability distributions on the line coincides with the $L^1$-distance between their distribution function. 
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     author = {S. S. Vallander},
     title = {Calculation of the {Wasserstein} distance between probability distributions on the line},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1973_18_4_a13/}
}
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S. S. Vallander. Calculation of the Wasserstein distance between probability distributions on the line. Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 4, pp. 824-827. http://geodesic.mathdoc.fr/item/TVP_1973_18_4_a13/