Geodesic
Two-sided estimates of Levy's metric
Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 2, pp. 239-250

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Along with the well-known Levy distance $L$ in the space of distribution functions, a new distance $\lambda$ in the space of characteristic functions is proposed. Upper and lower estimates of $L$, close to optimal ones, are constructed using $\lambda$. Various particular cases are considered. 
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     author = {V. M. Zolotarev and V. V. Senatov},
     title = {Two-sided estimates of {Levy's} metric},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {239--250},
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     volume = {20},
     number = {2},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1975_20_2_a1/}
}
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V. M. Zolotarev; V. V. Senatov. Two-sided estimates of Levy's metric. Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 2, pp. 239-250. http://geodesic.mathdoc.fr/item/TVP_1975_20_2_a1/