Affinity of entropy under ergodic decomposition
= Affinity of entropy under ergodic decomposition
If $\mu=\int\nu\,d\tau(\nu)$ is an <ergodic decomposition>, then the <Kolmogorov-Sinai entropy> satisfies $h_\mu(T)=\int h_\nu(T)\,d\tau(\nu)$.
= Affinity of entropy under ergodic decomposition
If $\mu=\int\nu\,d\tau(\nu)$ is an <ergodic decomposition>, then the <Kolmogorov-Sinai entropy> satisfies $h_\mu(T)=\int h_\nu(T)\,d\tau(\nu)$.