Abstract
A finite state stationary process is defined to be loosely block independent if long blocks are almost independent in the\(\overline f \) sense. We show that loose block independence is preserved under Kakutani equivalence and\(\overline f \) limits. We show directly that any loosely block independent process is the\(\overline f \) limit of Bernoulli processes and is a factor of a process which is Kakutani equivalent to a Bernoulli shift. The existing equivalence theory then yields that the loosely block independent processes are exactly the loosely Bernoulli (or finitely fixed) processes.
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Rahe, M., Swanson, L. Loose block independence. Israel J. Math. 38, 100–106 (1981). https://doi.org/10.1007/BF02761853
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DOI: https://doi.org/10.1007/BF02761853