Mean convergence theorems and weak laws of large numbers for double arrays of random variables
For an array of random variables indexed by two sequences of positive integers, this paper establishes first a mean convergence theorem for its weighted sum. A theorem for the weak laws of large numbers is also established for the weighted double sums of the array with random indices. Several examples are given to illustrate that the conditions in these theorems cannot be in general relaxed.
scientific article; zbMATH DE number 5134588
scientific article