A characterization of the existence of statistical limit of real-valued measurable functions (Q879238)
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scientific article; zbMATH DE number 5150266
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A characterization of the existence of statistical limit of real-valued measurable functions |
scientific article; zbMATH DE number 5150266 |
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A characterization of the existence of statistical limit of real-valued measurable functions (English)
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8 May 2007
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\textit{F. Móricz} [Analysis, München 24, No. 1, 1--18 (2004; Zbl 1062.40007)] has introduced a nondiscrete version of statistical convergence and called it statistical-1 limit. In the present paper the authors extend the definition of statistical limit to functions of several variables. A theorem of \textit{I. J. Schoenberg} [Am. Math. Mon. 66, 361--375, 562--563 (1959; Zbl 0089.04002)] is extended to multiple sequences as well as to statistical limit of functions of more variables. The theorems may be generalized even to vector-valued sequences or functions.
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multiple sequence
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convergence in Pringsheim's sense
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statistical convergence
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statistical boundedness
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measurable function in one- and several variables
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limit in Pringsheim's sense at \(\infty\)
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statistical limit at \(\infty\)
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Schoenberg's characterization theorem
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