Klesov O. Limit theorems for multiple sums of random variables

The thesis is devoted to the study of multiple sums of random variables for which a theory is constructed, analogous to the classical theory for usual sums. Criteria are found for the weak convergence of independent random variables, conditions are studied for the convergence and boundedness of multiple series, criteria are obtained for the integrability of weighted multiple sums, the asymptotics is obtained for the renewal process and function constructed by the random walk with multidimensional time, conditions are obtained for the Kotelnikoff-Shannon theorem for random fields.