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.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Bibliography
V. Bergelson. Ergodic Ramsey theory, Contemporary Mathematics, Vol.65, 1985, 63–87.
V. Bergelson, J. Rosenblatt. Joint ergodicity for group actions. To appear in Ergodic theory and Dynamical Systems.
H. Furstenberg. Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetical progressions. J. d’Analyse Math. 31, 1977, 204–256.
V. Krengel. Weakly Wandering Vectors and weakly independent partitions, Trans. AMS 164, 1972, 199–226.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer-Verlag
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/BFb0082821
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50174-9
Online ISBN: 978-3-540-45946-0
eBook Packages: Springer Book Archive
