On topological properties of the set of maldistributed sequences-Reference-Cited by-同舟云学术

On topological properties of the set of maldistributed sequences

Published:2020-11-01 Issue:2 Volume:12 Page:272-279
ISSN:2066-7752
Container-title:Acta Universitatis Sapientiae, Mathematica
language:en
Short-container-title:

Author:

Bukor József¹,Tóth János T.²

Affiliation:

1. Department of Informatics , J. Selye University , Komárno , Slovakia

2. Department of Mathematics , J. Selye University , Komárno , Slovakia

Abstract

Abstract The real sequence (x n ) is maldistributed if for any non-empty interval I, the set {n ∈𝕅 : x n ∈I} has upper asymptotic density 1. The main result of this note is that the set of all maldistributed real sequences is a residual set in the set of all real sequences (i.e., the maldistribution is a typical property in the sense of Baire categories). We also generalize this result.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.sciendo.com/pdf/10.2478/ausm-2020-0018

Reference12 articles.

1. [1] R. Alexander, Density and multiplicative structure of sets of integers, Acta Arith., 12 (1976), 321–332.

2. [2] J. A. Fridy, Statistical limit points, Proc. Amer. Math. Soc., 118 (1993), 1187–1192.

3. [3] P. Kostyrko, M. Mačaj, T. Šalát, O. Strauch, On statistical limit points, Proc. Amer. Math. Soc., 129 (2000), 2647–2654.

4. [4] P. Kostyrko, M. Mačaj, T. Šalát, O. Strauch, I-convergence and extremal I-limit points, Math. Slovaca, 55 (2005), 443–464.

5. [5] V. László, T. Šalát, The structure of some sequence spaces, and uniform distribution (mod 1), Periodica Math. Hung., 10 (1979), 89–98.

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Maldistributed sequences in metric spaces;Journal of Mathematical Analysis and Applications;2025-01

2. Typical Sequence of Real Numbers From the Unit Interval Has All Distribution Functions;International Journal of Analysis and Applications;2024-05-06