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

Year 2020, , 494 - 497, 02.04.2020

Harry I. Miller Leila Miller-van Wieren

https://doi.org/10.15672/hujms.712019

Cited By: 3

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.

Keywords

sequences, subsequences, statistical cluster points, statistical limit points

References

• [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.