On obtaining a stationary process isomorphic to a given process with a desired distribution

Let _e denote the set of distributions of all stationary, ergodic, aperiodic processes with a given finite state space, and let the metric on _e be Ornstein's process distance. Suppose is a subset of _e which is a in the weak topology and for which (µ _n ,)0 whenever { _n } is a sequence from _e converging weakly to a positive entropy measure in . It is shown that ifX is a stationary ergodic aperiodic process with entropy rate less than the entropy of one of the distributions in , thenX is isomorphic to a process whose distribution lies in . As special cases, one obtains the invulnerable source coding theorem of information theory and also the Grillenberger-Krengel theorem on the existence of a generator whose process has a desired marginal distribution.Research of author supported by NSF Grant ECS-78-21335.