Abstract
Those stationary stochastic processes measurably isomorphic to an independent process have been characterized by Ornstein and Weiss (6), (7), (8), as those satisfying a condition called “very weak Bernoulli”. A measure preserving transformation is often also continuous with respect to some natural topology. The topology which will most interest us here is that, on a countable state stochastic process, generated by the cylinder sets, i.e., if the outputs of the system are the symbols R1, R2, ..., we can view the underlying probability space as {R1, ...}z with its product topology.
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© 1981 Springer Science+Business Media New York
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Rudolph, D.J. (1981). A Characterization of Those Processes Finitarily Isomorphic to a Bernoulli Shift. In: Katok, A. (eds) Ergodic Theory and Dynamical Systems I. Progress in Mathematics, vol 10. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-6696-4_1
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DOI: https://doi.org/10.1007/978-1-4899-6696-4_1
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