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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On statistical limit points


Authors: P. Kostyrko, M. Macaj, T. Salát and O. Strauch
Journal: Proc. Amer. Math. Soc. 129 (2001), 2647-2654
MSC (2000): Primary 40A05, 11K31, 11B05
Published electronically: December 7, 2000
MathSciNet review: 1838788
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Abstract | References | Similar Articles | Additional Information

Abstract:

The set of all statistical limit points of a given sequence $x_n$is characterized as an $F_\sigma$-set. It is also characterized in terms of discontinuity points of distribution functions of $x_n$.


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Additional Information

P. Kostyrko
Affiliation: Department of Mathematics, Comenius University, SK-842 15 Bratislava, Slovakia
Email: kostyrko@fmph.uniba.sk

M. Macaj
Affiliation: Department of Mathematics, Comenius University, SK-842 15 Bratislava, Slovakia
Email: macaj@fmph.uniba.sk

T. Salát
Affiliation: Department of Mathematics, Comenius University, SK-842 15 Bratislava, Slovakia

O. Strauch
Affiliation: Mathematical Institute of the Slovak Academy of Sciences, Štefánikova 49, SK-814 73 Bratislava, Slovakia
Email: strauch@mat.savba.sk

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05891-3
PII: S 0002-9939(00)05891-3
Keywords: Statistically convergent sequence, statistical limit point, asymptotic density, distribution function
Received by editor(s): December 12, 1998
Received by editor(s) in revised form: January 10, 2000
Published electronically: December 7, 2000
Additional Notes: This work was supported in part by grants from VEGA No. 2/5123/98 and No. 1/4323/97
Communicated by: David Preiss
Article copyright: © Copyright 2000 American Mathematical Society