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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 49 Issue: 2

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

Harry I. Miller(International University of Sarajevo,)
Leila Miller-van Wieren(International University of Sarajevo,)0000-0002-7621-9231
Sayfa
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Yayın Tarihi
2020-04-02
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Fridy [Statistical limit points, Proc.
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Temel Bulgular & Veri:Soc., 1993] considered statistical cluster points and statistical limit points of a given sequence x.
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Sonuç & Katkı:Also, we show an analogous result for the statistical limit points of x.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

Miller, H. I., Wieren, L. M. (2020). Statistical cluster point and statistical limit point sets of subsequences of a given sequence. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 2. https://doi.org/10.15672/hujms.712019

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Kaynakça (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.