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Statistical convergence of sequences of functions with values in semi-uniform spaces. (English) Zbl 1463.54016

Summary: We study several kinds of statistical convergence of sequences of functions with values in semi-uniform spaces. Particularly, we generalize to statistical convergence the classical results of C. Arzelà, Dini and P. S. Alexandroff, as well as their statistical versions studied in [A. Caserta et al., Abstr. Appl. Anal. 2011, Article ID 420419, 11 p. (2011; Zbl 1242.40003); Appl. Math. Lett. 25, No. 10, 1447–1451 (2012; Zbl 1255.54010)].

MSC:

54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
40A30 Convergence and divergence of series and sequences of functions
40A35 Ideal and statistical convergence
54E15 Uniform structures and generalizations
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