<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

Online veröffentlicht: 15. Feb. 2023

Seitenbereich: 1 - 8

Eingereicht: 26. Juni 2021

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

Schlüsselwörter
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

Online veröffentlicht: 15. Feb. 2023

Seitenbereich: 1 - 8

Eingereicht: 26. Juni 2021

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

Schlüsselwörterrepresentations 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.

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