Abstract
An example is constructed of a two state stationary stochastic process (T, P) whose time zero partition P is weak Bernoulli under the shift, but which cannot be the image under a finitary coding of any independent process. A sufficient condition for a partition to be weak Bernoulli is developed, based on the rate of convergence of the conditional entropy $h(P|P_{ - j}^{ - 1})$ to $h(P,T)$.
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