In Markov process, an extremal reversible measure is an extremal invariant measure.

We consider a discrete-time temporally-homogeneous conservative Markov process. Ergodic theory of Markov process asserts that $m$ is an ergodic invariant probability measure if and only if $m$ is an extremal of the set of all invariant probability measures. On the other hand, Krein-Milman theorem asserts that a compact convex set in a Hausdorff locally-convex topological vector space is the closed convex hull of its extremals. In this paper, we show that extremality of reversible probability measure implies extremality of invariant probability measure. Using analogue of Dirichlet form, we modify a proof that in stochastic Ising model (Glauber dynamics), an extreme Gibbs state is an extreme invariant measure.