Statistical limit points

Author:
J. A. Fridy

Journal:
Proc. Amer. Math. Soc. **118** (1993), 1187-1192

MSC:
Primary 40C99

MathSciNet review:
1181163

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Abstract: Following the concept of a statistically convergent sequence , we define a statistical limit point of as a number that is the limit of a subsequence of such that the set does not have density zero. Similarly, a statistical cluster point of is a number such that for every the set does not have density zero. These concepts, which are not equivalent, are compared to the usual concept of limit point of a sequence. Statistical analogues of limit point results are obtained. For example, if is a bounded sequence then has a statistical cluster point but not necessarily a statistical limit point. Also, if the set has density one and is bounded on , then is statistically convergent.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1993-1181163-6

Keywords:
Natural density,
statistically convergent sequence

Article copyright:
© Copyright 1993
American Mathematical Society