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Weakly mixing actions of F have infinite subgroup actions which are Bernoulli

Part of the Lecture Notes in Mathematics book series (LNM,volume 1342)

Abstract

Let F be a finite field, and F the direct sum of countably many copies of F. Regarding F as a vector space over F, we extend the multiple recurrence theory of weakly mixing ℤ-actions to weakly mixing actions of F. From this we argue that such a weakly mixing action must have a subgroup action, isomorphic to F, that is Bernoulli.

Keywords

  • Finite Group
  • Finite Field
  • Multiple Recurrence
  • Finite Partition
  • Subgroup Action

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliography

  1. V. Bergelson. Ergodic Ramsey theory, Contemporary Mathematics, Vol.65, 1985, 63–87.

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© 1988 Springer-Verlag

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Bergelson, V., Rudolph, D.J. (1988). Weakly mixing actions of F have infinite subgroup actions which are Bernoulli. In: Alexander, J.C. (eds) Dynamical Systems. Lecture Notes in Mathematics, vol 1342. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082821

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  • DOI: https://doi.org/10.1007/BFb0082821

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50174-9

  • Online ISBN: 978-3-540-45946-0

  • eBook Packages: Springer Book Archive