On one case of the limit theorem of probability calculation

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, as a result of which the Lyapunov conditions known in science were obtained. Further work on the issue under consideration was reduced mainly to the development of new methods for proving the theorem on the limit of probability and did not yield a significant expansion of Lyapunov’s conditions. Therefore, it is natural to pose and try to solve the problem of extending the Lyapunov conditions, which is what this work is devoted to.