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Statistical limits of measurable functions. (English) Zbl 1062.40007

The concept of statistical limit at infinity of a measurable real or complex valued function is introduced, as the analogous nondiscrete correspondent of the well-known concept of statistical convergence of a sequence of numbers. Then, various applications of this concept are considered, amongst them the statistical convergence of Fourier transforms.

MSC:

40C10 Integral methods for summability
40C15 Function-theoretic methods (including power series methods and semicontinuous methods) for summability
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
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