On topological properties of the set of maldistributed sequences

József Bukor; János T. Tóth

doi:10.2478/ausm-2020-0018

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On topological properties of the set of maldistributed sequences

Acta Universitatis Sapientiae, Mathematica

Volume 12 (2020): Issue 2 (November 2020)

By: József Bukor and János T. Tóth

Open Access

|Dec 2020

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.

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Articles in this issue

DOI: https://doi.org/10.2478/ausm-2020-0018 | Journal eISSN: 2066-7752

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Language: English

Page range: 272 - 279

Submitted on: Feb 20, 2019

Published online: Dec 2, 2020

Published in print: Nov 1, 2020

Published by: Sapientia Hungarian University of Transylvania

In partnership with: Paradigm Publishing Services

Keywords:

maldistributed sequence,

MSC:

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© 2020 József Bukor, János T. Tóth, published by Sapientia Hungarian University of Transylvania
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 12 (2020): Issue 2 (November 2020)