R ‐Theory for Markov Chains on a Topological State Space I

~z"P"(x, A) of the n-step transition probabilities, we follow Tweedie [6] in using 1 the following form of irreducibility: there is a probcbility measure M on g for which M(A)>0 implies that G~(x,A)>O for all x~g, and M(A)=0 implies M{y: G~(y,A)>O}=O. We denote {A~,~: M(A)>0} by Y+; "almost all x" shall henceforth be with respect to this M. Tweedie [6] has proved the following solidarity results for such a chain (cs Theorems A and C of [4]):