On statistical limit points
HTML articles powered by AMS MathViewer
- by P. Kostyrko, M. Mačaj, T. Šalát and O. Strauch PDF
- Proc. Amer. Math. Soc. 129 (2001), 2647-2654 Request permission
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 $x_n$.References
- Daniel Berend, Michael D. Boshernitzan, and Grigori Kolesnik, Distribution modulo $1$ of some oscillating sequences. II, Israel J. Math. 92 (1995), no. 1-3, 125–147. MR 1357748, DOI 10.1007/BF02762073
- J. A. Fridy, Statistical limit points, Proc. Amer. Math. Soc. 118 (1993), no. 4, 1187–1192. MR 1181163, DOI 10.1090/S0002-9939-1993-1181163-6
- H. Halberstam and K. F. Roth, Sequences. Vol. I, Clarendon Press, Oxford, 1966. MR 0210679
- L. Kuipers and H. Niederreiter, Uniform distribution of sequences, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. MR 0419394
- G. Myerson, A sampler of recent developments in the distribution of sequences, Number theory with an emphasis on the Markoff spectrum (Provo, UT, 1991) Lecture Notes in Pure and Appl. Math., vol. 147, Dekker, New York, 1993, pp. 163–190. MR 1219333
- D. P. Parent, Exercises in number theory, Problem Books in Mathematics, Springer-Verlag, New York, 1984. Coauthored by D. Barsky, F. Bertrandias, G. Christol, A. Decomps, H. Delange, J.-M. Deshouillers, K. Lamèche-Gérardin, J. Lagrange, J.-L. Nicolas, M. Pathiaux, G. Rauzy and M. Waldschmidt; With a preface by Ch. Pisot; Translated from the French. MR 759342, DOI 10.1007/978-1-4757-5194-9
- I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959), 361–375. MR 104946, DOI 10.2307/2308747
- Oto Strauch, Uniformly maldistributed sequences in a strict sense, Monatsh. Math. 120 (1995), no. 2, 153–164. MR 1348367, DOI 10.1007/BF01585915
- O. Strauch, On set of distribution functions of a sequence. In: Proc. Conf. Analytic and Elementary Number Theory, In Honor of E. Hlawka’s 80th Birthday, Vienna, July 18-20, 1996, Universität Wien and Universität für Bodenkultur, (W. G. Nowak and J. Schoißengeier, eds.) Vienna, 1997, 214–229.
Additional Information
- P. Kostyrko
- Affiliation: Department of Mathematics, Comenius University, SK-842 15 Bratislava, Slovakia
- Email: kostyrko@fmph.uniba.sk
- M. Mačaj
- Affiliation: Department of Mathematics, Comenius University, SK-842 15 Bratislava, Slovakia
- Email: macaj@fmph.uniba.sk
- T. Šalát
- 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
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 2647-2654
- MSC (2000): Primary 40A05, 11K31, 11B05
- DOI: https://doi.org/10.1090/S0002-9939-00-05891-3
- MathSciNet review: 1838788