Monotonicity of normalized block entropy
= Monotonicity of normalized block entropy
For a stationary process associated with a finite-entropy <measurable partition>, $H_\mu(\xi_0^{n-1})/n$ is non-increasing. The increments $c_k=H_\mu(\xi\mid\bigvee_{j=1}^kT^{-j}\xi)$ are non-increasing by <conditioning reduces entropy>, and the chain rule gives $H_\mu(\xi_0^{n-1})=\sum_{k=0}^{n-1}c_k$. Averages of a decreasing sequence are decreasing.