Loose block independence
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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.
KeywordsBlock Code Independent Process Bernoulli Shift Conditional Measure Generate Partition
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- 6.Benjamin Weiss,Equivalence of Measure Preserving Transformations, Lecture Notes, Institute for Advanced Studies, Hebrew University of Jerusalem, 1976.Google Scholar