In a paper entitled "Ergodic theorems for infinite probabilistic tables," Paz studies the ergodic properties of non-homogeneous Markov chains with countably infinite state space. This note is to draw attention to the fact that Paz's theory is easily extended to arbitrary state spaces.
Richard W. Madsen. "A Note on some Ergodic Theorems of A. Paz." Ann. Math. Statist. 42 (1) 405 - 408, February, 1971. https://doi.org/10.1214/aoms/1177693534