TYPES OF CONVERGENCE OF RANDOM VARIABLES. CONVERGENCE OF DISTRIBUTIONS

In the course of mathematical analysis, various approximations of sequences of functions are considered: smooth approximation, approximation at almost all points, approximation by measure, mean square approximation, and other similar approximations. Similarly, in probability theory, sequences of random variables and, at the same time, various approximations of sequences of distribution functions are considered. These approximations serve as the basis for limit theorems in probability theory.