Suppose ${X_n}$ is a Markov process taking values in some arbitrary space $(S, varphi)$ with n-stemp transition probability $$ P^{(n)}(x, B) = Prob(X_n in B$mid$X_0 = x), x in X, B in varphi.$$</TEX> We shall call a Markov process with transition probabilities $P{(n)}(x, B)$ $phi$-irreducible for some non-trivial $sigma$-finite measure $phi$ on $varphi$ if whenever $phi(B) > 0$, $$ sum^{infty}_{n=1}{2^{-n}P^{(n)}}(x, B) > 0, for every x in S.$$ A non-trivial $sigma$-finite measure $pi$ on $varphi$ is called invariant for ${X_n}$ if $$ int{P(x, B)pi(dx) = pi(B)}, B in varphi $$.