<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

Publicado en línea: 15 feb 2023

Páginas: 1 - 8

Recibido: 26 jun 2021

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

Palabras clave
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

Publicado en línea: 15 feb 2023

Páginas: 1 - 8

Recibido: 26 jun 2021

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

Palabras claverepresentations 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.

Palabras clave
representations of real numbers, discrete distributions, digits, frequency, Hausdorff dimension