On one case of the limit theorem of the calculus of probability

Abstract

This work refers to the consideration of the case of a limit theorem with respect to independent variables—a case that was developed by Academicians Markov and Lyapunov, resulting in the conditions known in science as Lyapunov's conditions. Further work on the issue under consideration was mainly reduced to developing new methods of proving the limit probability theorem and did not yield a significant extension of Lyapunov's conditions. It is therefore natural to pose and attempt to solve the problem of extending Lyapunov's conditions, to which this work is devoted.

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