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

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