  We propose a generalization of the asymptotic equipartition property to
discrete sources with an ambiguous alphabet, and prove that it holds for
irreducible stationary Markov sources with an arbitrary distinguishability
relation. Our definition is based on the limiting behavior of graph parameters
appearing in a recent dual characterization of the Shannon capacity, evaluated
at subgraphs of strong powers of the confusability graph induced on
high-probability subsets. As a special case, our results give an
information-theoretic interpretation of the graph entropy rate of such sources.
