<abstract xmlns="http://www.w3.org/1999/xhtml">The real sequence (x<italic>n</italic>) is maldistributed if for any non-empty interval I, the set {<italic>n</italic> ∈𝕅 : x<italic>n</italic> ∈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.</abstract>

The real sequence (xn) is maldistributed if for any non-empty interval I, the set {n ∈𝕅 : xn ∈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.

On topological properties of the set of maldistributed sequences

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"On topological properties of the set of maldistributed sequences"}

The real sequence (xn) is maldistributed if for any non-empty interval I, the set {n ∈𝕅 : xn ∈I} has upper asymptotic density 1. The main result of this note...

On topological properties of the set of maldistributed sequences

Published Online: Dec 02, 2020

Page range: 272 - 279

Received: Feb 20, 2019

DOI: https://doi.org/10.2478/ausm-2020-0018

Keywords
maldistributed sequence, weighted density, Baire category

© 2020 József Bukor et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On topological properties of the set of maldistributed sequences

Published Online: Dec 02, 2020

Page range: 272 - 279

Received: Feb 20, 2019

DOI: https://doi.org/10.2478/ausm-2020-0018

Keywordsmaldistributed sequence, weighted density, Baire category

© 2020 József Bukor et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
maldistributed sequence, weighted density, Baire category