Let $(X,T)$ and $(Y,S)$ be two intrinsically ergodic system with the same topological entropy i.e. $\exists ! \mu, \exists ! \nu$ measures of maximal entropy such that $h_\mu(T)=h_{top}(T)=h_{top}(S)=h_\nu(S)$. Proove that if $\pi:(X,T)\rightarrow (Y,S)$ is a factor i.e. $\pi$ is continuous, surjective and $\pi \circ T=S\circ \pi$, then $\pi\mu=\nu$.
Any help will be appreciated.