Harry I. Miller

7098

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

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.
Keywords:

sequences, subsequences, statistical cluster points statistical limit points,

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  • [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.
Hacettepe Journal of Mathematics and Statistics-Cover
  • Yayın Aralığı: 6
  • Başlangıç: 2002
  • Yayıncı: Hacettepe Üniversitesi Fen Fakultesi
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