UNIFORM STATISTICAL CONVERGENCE OF DOUBLE SUBSEQUENCES
In the [3] is proven that sequence Sij uniformly statistically converges to L if and only if it there is a subset A of the set N × N uniform density zero and subsequence S (x) defined by, Sij (x) = Sij for (i, j) ∈ Ac, converges to L, in the Pringsheim’s sense. In this paper it is proven that analog is valid for subsequence S (x) provided that for each N and i 6 N ∨ j 6 N is a set of all Sij (x) finite set. Is generally valid: If the subsequence S (x) uniformly statistically converges to L, then, there is a subset A of the set N× N uniform density zero and subsequence S (y) defined by, Sij (y) = Sij (x) for (i, j) ∈ Ac, converges to L, in the Pringsheim’s sense. If there is a subset A of the set N × N uniform density zero and subsequence S (y) defined by, Sij (y) = Sij (x) for (i, j) ∈ Ac, such that lim i→∞ ( lim j→∞ Sij (y)) = L, then, the subsequence S (x) uniformly statistically converges to L.