BOUNDARY MEASURES OF MARKOV-CHAINS

It is known that each Markov chain has associated with it a polytope a nd a family of Markov measures indexed by the interior points of the p olytope. Measure-preserving factor maps between Markov chains must pre serve the associated families. In the present paper, we augment this s tructure by identifying measures corresponding to points on the bounda ry of the polytope. These measures are also preserved by factor maps. We examine the data they provide and give examples to illustrate the u se of this data in ruling out the existence of factor maps between Mar kov chains.