## 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

### Keywords:

statistical convergence; Lebesgue space; Tauberian theorems

Zbl 0588.40001
Full Text:

### References:

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