Let $T:X \rightarrow X$ be a measure-preserving transformation of the probability space $(X,B,\mu)$. ($X$ is a topological space). If $K\subset X$ is a compact and invariant set, show that $h_{\mu}(f|K)=h_{\mu}(f)$. Here $h_{\mu}(.)$ denote entropy a measure-preserving transformation.
Best.
