Relatively Finitely Determined Implies Relatively Very Weak Bernoulli

Abstract

In the isomorphism theory of Bernoulli shifts, the or Hamming distance plays an important role. Two finite state stationary processes are close in the metric if, on the average, strings from one process can be matched with strings from the other process so that their outputs agree with high frequency. Since such agreement must hold in the arbitrarily distant future, it might at first seem difficult to control the pairing.