On Uniform Distribution Modulo 1 and Functional Convergence

Milan Paštéka

doi:10.2478/udt-2024-0004

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On Uniform Distribution Modulo 1 and Functional Convergence

Uniform distribution theory

Volume 19 (2024): Issue 1-2 (December 2024)

By: Milan Paštéka

Open Access

|Feb 2025

Abstract

In this note, we study the convergence of functional sequences. A criterion for uniform distribution mod 1 is derived. Then we study the partitions, block sequences and the uniform distribution preserving mappings. In the last part, we prove that to each one to one sequence dense in [0, 1] a regular matrix summation method such that this sequence is uniformly distributed mod 1 with respect to this method exists.

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Articles in this issue

DOI: https://doi.org/10.2478/udt-2024-0004 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X

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Language: English

Page range: 33 - 42

Submitted on: Apr 8, 2024

Accepted on: Jun 20, 2024

Published on: Feb 24, 2025

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

uniform distribution,

asymptotic density,

matrix density,

uniform distribution preserving mapping

Related subjects:

Mathematics,

Algebra and number theory,

Discrete mathematics,

Probability and statistics,

Numerical and computational mathematics

© 2025 Milan Paštéka, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 19 (2024): Issue 1-2 (December 2024)