Statistically convergent double sequences. (English) Zbl 1040.40001

Summary: We introduce the notion of density of subsets of \(N\times N\). Using this concept we introduce the notions of statistically convergent double sequences and statistically Cauchy double sequences. The decomposition theorem is proved. The inclusion relations are obtained. We show that the bounded statistically convergent sequence spaces in Pringsheim’s sense are not separable. A relation between strongly \(p\)-Cesàro summability of double sequences and bounded statistically convergent double sequences is established.


40A05 Convergence and divergence of series and sequences
40B05 Multiple sequences and series
46A45 Sequence spaces (including Köthe sequence spaces)