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Directional Entropy and Pinsker $\sigma $-Algebra for $\mathbb {Z}^{2}$-Actions

Runju Wei , Leiye Xu , Xiaomin Zhou

Communications in Mathematics and Statistics ›› : 1 -18.

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Communications in Mathematics and Statistics ›› : 1 -18. DOI: 10.1007/s40304-023-00369-z
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Directional Entropy and Pinsker $\sigma $-Algebra for $\mathbb {Z}^{2}$-Actions

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Abstract

In this paper, we study the directional entropy along irrational directions in $\mathbb {R}^2$ and present the structure of directional Pinsker $\sigma $-algebra of $\mathbb {Z}^2$-MPSs.

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$\sigma $-algebra')">Directional Pinsker $\sigma $-algebra / Directional entropy

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Runju Wei, Leiye Xu, Xiaomin Zhou. Directional Entropy and Pinsker $\sigma $-Algebra for $\mathbb {Z}^{2}$-Actions. Communications in Mathematics and Statistics 1-18 DOI:10.1007/s40304-023-00369-z

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Funding

National Natural Science Foundation of China(12031019)

Fundamental Research Funds for the Central Universities(2020kfyXJJS036)

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