Estimation of proximity of distributions of sequential sums of independent identically distributed random vectors

Let be a distribution in, let be the n-fold convolution of with itself, and let. It is proved that where depends on certain characteristics of.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 97, pp. 83–87, 1980.In conclusion, the author expresses his gratitude to I. A. Ibragimov for his interest in the paper.