Geodesic
A~smoothing inequality for estimations of Levy--Prokhorov distance
Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 1, pp. 3-12

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An analogue of well known Berry–Esseen inequality for Levy–Prokhorov metric in proved. 
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     author = {V. V. Yurinskii},
     title = {A~smoothing inequality for estimations of {Levy--Prokhorov} distance},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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V. V. Yurinskii. A~smoothing inequality for estimations of Levy--Prokhorov distance. Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 1, pp. 3-12. http://geodesic.mathdoc.fr/item/TVP_1975_20_1_a0/