Information theoretic properties of stochastic processes on partition fibers

In a probability space, the partition fiber relative to a probability vector v is the set of all ordered partitions of that space, the probabilities of whose atoms are the components of v. We define as an stochastic process any ordered pair consisting of a measure preserving transformation of the probability space, and an ordered finite partition of this space. To each stochastic process one assigns the usual Kolmogorov-Sinai relative entropy. The main result of this dissertation is that for each ergodic measure preserving invertible transformation T of an atomless probability space, and for each probability vector v, there are ordered partitiers in the partition fiber relative to v.such that the relative entropy on the resulting stochastic processes assumes any value between zero an the least of H(v) and h(T). This result is arrived at by generalizing to atomless spaces techniques used by D.S.Ornstein in [1970-Ornstein].