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Statistical convergence of functional sequences. (English) Zbl 1378.40003

The authors study the statistical convergence in Lebesgue spaces \(L_p\). They introduce the concept of statistical fundamentality in \(L_p\) and prove that statistical fundamentality and statistical convergence are equivalent in \(L_p\). They also prove that analogues of some Tauberian theorems in [J. A. Fridy, Analysis 5, 301–313 (1985; Zbl 0588.40001)] are valid in their case.

MSC:

40A35 Ideal and statistical convergence
40J05 Summability in abstract structures
40E05 Tauberian theorems

Citations:

Zbl 0588.40001
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References:

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