P(\varphi,f)=\sup_{\mu \in \mathcal{M}_f} h_{\mu}(f)+\int \varphi \;d\mu\lim_{n\to\infty}\frac1n\sum_{i=0}^{n-1}\varphi (f^i(x))\to \mathbb{E}(\varphi\mid \mathcal{I})(x)(h^u_{x_1,x_2})_*\mu_{x_1}^u=\mu_{x_2}^uLua’s Webpage
ergodic theory, formalization, 🐱s