Let $(X_i)_{i\ge1}$ be stochstic process with finite space $X$. Show that if one of the limits
exists, then also the other limits exist and all 3 coincide. H is the entropy.
I have found a proof (see underneath), but this one is only for stochastic processes. Is there a possibility, without assuming the process is stationary?
see $\rightarrow$ Stochastic process entropy rate limit