# Uniform Limit Theorems for Sums of Independent Random Variables

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*T. V. Arak; A. Yu. Zaĭtsev*

Among the diverse constructions studied in modern probability
theory, the scheme for summation of independent random variables
occupies a special place. In the study of even this comparatively
simple scheme it is possible to become familiar with the fundamental
regularities characterizing the cumulative influence of a large number
of random factors. Further, this abstract model is useful in many
important practical situations.

This book is devoted to the study of distributions of sums of independent
random variables with minimal restrictions imposed on their distributions. The
authors assume either that the distributions of the terms are concentrated on
some finite interval to within a small mass, or that all the terms have the
same, but arbitrary, distribution (or other conditions not connected with
moment restrictions are introduced). Surprisingly, very substantive results
are possible even under such a general statement of the problems.