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On statistically convergent series. (English) Zbl 0966.40003

The concept of statistical convergence of sequences was introduced by H. Fast [Sur la convergence statistique, Colloq. Math. 2, 241-244 (1951; Zbl 0044.33605)] and developed by other authors. In this paper the author extends this concept to the concept of statistical convergence of infinite series in analogy with the usual convergence. Some fundamental properties of statistically convergent series are established here and illustrated by several suitable chosen examples.

MSC:

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

Citations:

Zbl 0044.33605
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