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Journals / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 2

Statistical cluster point and statistical limit point sets of subsequences of a given sequence

Harry I. Miller
Pages
494–497
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Also, we show an analogous result for the statistical limit points of x.

📌 3 Key Takeaways

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Objective & Hypothesis:Fridy [Statistical limit points, Proc.
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Key Findings & Data:Soc., 1993] considered statistical cluster points and statistical limit points of a given sequence x.
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Conclusion & Impact:Also, we show an analogous result for the statistical limit points of x.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:sequences · subsequences · statistical cluster points

Abstract

J.A. Fridy [Statistical limit points, Proc. Amer. Math. Soc., 1993] considered statistical cluster points and statistical limit points of a given sequence x. Here we show that almost all subsequences of x have the same statistical cluster point set as x. Also, we show an analogous result for the statistical limit points of x.

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Cite This Article

Miller, H. I. (2022). Statistical cluster point and statistical limit point sets of subsequences of a given sequence. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 2, 494–497. https://ajindex.com/articles/529669

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References (5)

  1. J.A. Fridy, Statistical limit points, Proc. Amer. Math. Soc. 118 1187–1192, 1993
  2. H.I. Miller, Measure theoretical subsequence characterization of statistical conver- gence, Trans. Amer. Math. Soc. 347 (5) 1811–1819, 1995
  3. H.I. Miller and L. Miller-Van Wieren, Some statistical cluster point theorems, Hacet. J. Math. Stat. 44 (6) 1405–1409, 2015
  4. P. Kostyrko, M. Mačaj, T. Šalat, and O. Strauch, On statistical limit points, Proc. Amer. Math. Soc. 129 (9), 2647–2654, 2000
  5. J.C. Oxtoby, Measure and Category: A survey of the analogies between topological and measure spaces. Second edition, Springer-Verlag, New York-Berlin,1980.