Geodesic
Improved multivariate version of the second Kolmogorov's uniform limit theorem
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 28, Tome 486 (2019), pp. 71-85

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The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent summands by the infinitely divisible laws may be transferred to the estimation of the closeness of distributions on convex polyhedra. 
@article{ZNSL_2019_486_a4,
     author = {F. G\"otze and A. Yu. Zaitsev and D. Zaporozhets},
     title = {Improved multivariate version of the second {Kolmogorov's} uniform limit theorem},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {71--85},
     publisher = {mathdoc},
     volume = {486},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_486_a4/}
}
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F. Götze; A. Yu. Zaitsev; D. Zaporozhets. Improved multivariate version of the second Kolmogorov's uniform limit theorem. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 28, Tome 486 (2019), pp. 71-85. http://geodesic.mathdoc.fr/item/ZNSL_2019_486_a4/