Geodesic
On a rate of convergence of empirical measures
Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part X, Tome 158 (1987), pp. 45-48

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For the Kantorovich-Rubinshtein metric we investigated the rate of convergence to zero of the average distance of an empirical measure to the distribution of a general collection depending on the massiveness of the compactum on which this distribution is concentrated. 
@article{ZNSL_1987_158_a4,
     author = {V. V. Volchaninov},
     title = {On a rate of convergence of empirical measures},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {45--48},
     publisher = {mathdoc},
     volume = {158},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_158_a4/}
}
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V. V. Volchaninov. On a rate of convergence of empirical measures. Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part X, Tome 158 (1987), pp. 45-48. http://geodesic.mathdoc.fr/item/ZNSL_1987_158_a4/