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On variations via statistical convergence. (English) Zbl 1425.62008

Starting from the concept of statistical convergence of a sequence of real numbers, related concepts, such as a statistical Cauchy sequence, statistical limit superior/inferior, statistical bounded sequence are stated. Then, several definitions for the notion of variability of functions or sequences are given, as e.g. regularly varying, rapidly varying. Based on the statistical convergence, statistical analogues of the standard variability concepts are formulated. The notion of the statistical variability is studied, and several known and new results are presented on the properties and relations arising in statistical varying sequences of positive numbers.

MSC:

62A01 Foundations and philosophical topics in statistics
40A35 Ideal and statistical convergence
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