Representations of Real Numbers Induced by Probability Distributions on ℕ

Jörg Neunhäuserer

doi:10.2478/tmmp-2022-0014

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Representations of Real Numbers Induced by Probability Distributions on ℕ

Tatra Mountains Mathematical Publications

Volume 82 (2022): Issue 2 (December 2022)

By: Jörg Neunhäuserer

Open Access

|Feb 2023

Abstract

We observe that a probability distribution supported by ℕ, induces a representation of real numbers in [0, 1) with digits in ℕ. We first study the Hausdorff dimension of sets with prescribed digits with respect to these representations. Then, we determine the prevalent frequency of digits and the Hausdorff dimension of sets with prescribed frequencies of digits. As examples, we consider the geometric distribution, the Poisson distribution and the zeta distribution.

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Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2022-0014 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 1 - 8

Submitted on: Jun 26, 2021

Published on: Feb 15, 2023

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

representations of real numbers,

discrete distributions,

digits,

Related subjects:

© 2023 Jörg Neunhäuserer, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 82 (2022): Issue 2 (December 2022)