Hausdorff dimension of sets defined by almost convergent binary expansion sequences
Glasgow mathematical journal, Tome 65 (2023) no. 2, pp. 450-456
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In this paper, we study the Hausdorff dimension of sets defined by almost convergent binary expansion sequences. More precisely, the Hausdorff dimension of the following set\begin{align*} \bigg\{x\in[0,1)\;:\;\frac{1}{n}\sum_{k=a}^{a+n-1}x_{k}\longrightarrow\alpha\textrm{ uniformly in }a\in\mathbb{N}\textrm{ as }n\rightarrow\infty\bigg\} \end{align*}is determined for any $ \alpha\in[0,1] $. This completes a question considered by Usachev [Glasg. Math. J. 64 (2022), 691–697] where only the dimension for rational $ \alpha $ is given.
Song, Qing-Yao. Hausdorff dimension of sets defined by almost convergent binary expansion sequences. Glasgow mathematical journal, Tome 65 (2023) no. 2, pp. 450-456. doi: 10.1017/S0017089523000046
@article{10_1017_S0017089523000046,
author = {Song, Qing-Yao},
title = {Hausdorff dimension of sets defined by almost convergent binary expansion sequences},
journal = {Glasgow mathematical journal},
pages = {450--456},
year = {2023},
volume = {65},
number = {2},
doi = {10.1017/S0017089523000046},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089523000046/}
}
TY - JOUR AU - Song, Qing-Yao TI - Hausdorff dimension of sets defined by almost convergent binary expansion sequences JO - Glasgow mathematical journal PY - 2023 SP - 450 EP - 456 VL - 65 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089523000046/ DO - 10.1017/S0017089523000046 ID - 10_1017_S0017089523000046 ER -
%0 Journal Article %A Song, Qing-Yao %T Hausdorff dimension of sets defined by almost convergent binary expansion sequences %J Glasgow mathematical journal %D 2023 %P 450-456 %V 65 %N 2 %U http://geodesic.mathdoc.fr/articles/10.1017/S0017089523000046/ %R 10.1017/S0017089523000046 %F 10_1017_S0017089523000046
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