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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.17430 |
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Table of Contents:
- In this paper, we study the Lebesgue structure of the distribution of a random variable given in terms of a continued fraction with a two-symbol alphabet $\{\frac{1}{2}, 1\}$, also known as $A_2$-fractions. We establish necessary and sufficient conditions for the distribution to be discrete and provide some sufficient conditions for its singularity. We also explore non-trivial metric properties of the $A_2$-representation with the specified alphabet.