On statistical limit points (Q2716108)
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scientific article; zbMATH DE number 1602165
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On statistical limit points |
scientific article; zbMATH DE number 1602165 |
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On statistical limit points (English)
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6 June 2001
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statistically convergent sequence
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statistical limit point
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asymptotic density
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distribution function of a sequence
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A real number \(x\) is said to be a statistical limit point of the sequence \(x_{n}\) if there exists a subsequence \(x_{k_{n}}\), \(n=1,2,\dots\), such that \(\lim_{n \to \infty} x_{k_{n}}=x\) and the set of indices \(k_{n}\) has a positive upper asymptotic density. The paper gives a characterization of the set of all statistical limit points of a given sequence \(x_{n}\) by means of \(F_{\sigma}\) sets.
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