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# Entropy Zero $\times$ Bernoulli Processes are Closed in the $\bar d$-Metric

Paul Shields and J.-P. Thouvenot
The Annals of Probability
Vol. 3, No. 4 (Aug., 1975), pp. 732-736
Stable URL: http://www.jstor.org/stable/2959337
Page Count: 5
An entropy zero $\times$ Bernoulli process is a stationary finite state process whose shift transformation is the direct product of an entropy zero transformation and a Bernoulli shift. We show that the class of such transformations which are ergodic is closed in the $\bar{d}$-metric. The $\bar{d}$-metric measures how closely two processes can be joined to form a third stationary process.