<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

Representations of Real Numbers Induced by Probability Distributions on ℕ

Tatra Mountains Mathematical Publications

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

{"article-title":"Representations of Real Numbers Induced by Probability Distributions on ℕ"}

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...

Representations of Real Numbers Induced by Probability Distributions on ℕ

Published Online: Feb 15, 2023

Page range: 1 - 8

Received: Jun 26, 2021

DOI: https://doi.org/10.2478/tmmp-2022-0014

Keywords
representations of real numbers, discrete distributions, digits, frequency, Hausdorff dimension

© 2022 Jörg Neunhäuserer, published by Sciendo

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

Representations of Real Numbers Induced by Probability Distributions on ℕ

Published Online: Feb 15, 2023

Page range: 1 - 8

Received: Jun 26, 2021

DOI: https://doi.org/10.2478/tmmp-2022-0014

Keywordsrepresentations of real numbers, discrete distributions, digits, frequency, Hausdorff dimension

© 2022 Jörg Neunhäuserer, published by Sciendo

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

Keywords
representations of real numbers, discrete distributions, digits, frequency, Hausdorff dimension