<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

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{"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

Publicado en línea: 02 dic 2020

Páginas: 272 - 279

Recibido: 20 feb 2019

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

Palabras clave
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

Publicado en línea: 02 dic 2020

Páginas: 272 - 279

Recibido: 20 feb 2019

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

Palabras clavemaldistributed 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.

Palabras clave
maldistributed sequence, weighted density, Baire category