A-Statistical Convergence of Subsequence of Double Sequences

Miller, Harry I.

Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 727-739

Résumé

The concept of statistical convergence of a sequence was first introduced by H. Fast [7] in 1951. Recently, in the literature, the concept of statistical convergence of double sequences has been studied. The main result in this paper is a theorem that gives meaning to the statement: $s={s_{ij}}$ converges statistically $A$ to $L$ if and only if "most" of the "subsequences" of $s$ converge to $L$ in the ordinary sense. The results presented here are analogue of theorems in [12], [13] and [6] and are concerned with $A$ statistical convergence, first introduced by Freedman and Sember [8]. Other related problems are considered.