  We study one-sided Markov shifts, corresponding to positively recurrent
Markov chains with countable (finite or infinite) state spaces. The following
classification problem is considered: when two one-sided Markov shifts are
isomorphic up to a measure preserving isomorphism In this paper we solve the
problem for the class of rho-uniform (or finitely rho-Bernoulli) one-sided
Markov shifts considered in Ru_6
  We show that every ergodic rho-uniform Markov shift T can be represented in a
canonical form T = T_G by means of a canonical (uniquely determined by T)
stochastic graph G. In the canonical form, two such shifts T_{G_1} and T_{G_2}
are isomorphic if and only if their canonical stochastic graphs G_1 and G_2 are
isomorphic.
