Geodesic
Proximity of probability distributions in terms of Fourier--Stieltjes transforms
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 71 (2016) no. 6, pp. 1021-1079

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A survey is given of some results on smoothing inequalities for various probability metrics (in particular, for the Kolmogorov distance), and some analogues of these results in the class of functions of bounded variation are presented. Bibliography: 61 titles.
Keywords: probability metrics, smoothing inequalities. 
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     author = {S. G. Bobkov},
     title = {Proximity of probability distributions in terms of {Fourier--Stieltjes} transforms},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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S. G. Bobkov. Proximity of probability distributions in terms of Fourier--Stieltjes transforms. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 71 (2016) no. 6, pp. 1021-1079. http://geodesic.mathdoc.fr/item/RM_2016_71_6_a1/