On a theorem of Dan Rudolph. I

Twenty years ago Dan Rudolph gave a seminar talk at the University of Maryland in which he discussed his discovery that if one restricts the shift invariant measures on a finite alphabet shift space to have entropy greater than or equal to c > 0, then the generic measure there defines a process that has entropy c and is isomorphic to a Bernoulli shift. He never published a proof of this theorem. In the following note we will present a proof of this result.