Geodesic
Some modifications of the Dudley metric
Zapiski Nauchnykh Seminarov POMI, Continuity and stability in the problems of probability theory and mathematical statistics, Tome 61 (1976), pp. 17-24

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Upper and lower bounds are obtained for the modified Dudley metric in terms of the Levy–Prokhorov metric. 
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     author = {N. V. Grigorevskii and I. S. Shiganov},
     title = {Some modifications of the {Dudley} metric},
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     volume = {61},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_61_a1/}
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N. V. Grigorevskii; I. S. Shiganov. Some modifications of the Dudley metric. Zapiski Nauchnykh Seminarov POMI, Continuity and stability in the problems of probability theory and mathematical statistics, Tome 61 (1976), pp. 17-24. http://geodesic.mathdoc.fr/item/ZNSL_1976_61_a1/