Israel Journal of Mathematics

, Volume 38, Issue 1–2, pp 100–106 | Cite as

Loose block independence

  • Maurice Rahe
  • Laif Swanson


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.


Block Code Independent Process Bernoulli Shift Conditional Measure Generate Partition 
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Copyright information

© The Weizmann Science Press of Israel 1981

Authors and Affiliations

  • Maurice Rahe
    • 1
  • Laif Swanson
    • 1
  1. 1.Department of MathematicsTexas A&M UniversityCollege StationUSA

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