Let $M\in\{0,1\}^{A\times A}$ be a finite irreducible zero-one matrix over a finite alphabet $A$, and let $\Sigma_M\subset A^{\mathbb Z}$ be the associated two-sided topological Markov chain. Then
paragraph
admin
\begin{align*}
h_{\mathrm{top}}(\sigma|_{\Sigma_M})=\sup\{h_\mu(\sigma): \mu \text{ is a } \sigma\text{-invariant Borel probability measure on }\Sigma_M\}.
\end{align*}