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Pointwise theorems for amenable groups


Author: Elon Lindenstrauss
Journal: Electron. Res. Announc. Amer. Math. Soc. 5 (1999), 82-90
MSC (1991): Primary 28D15
DOI: https://doi.org/10.1090/S1079-6762-99-00065-7
Published electronically: June 30, 1999
MathSciNet review: 1696824
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Abstract: In this paper we describe proofs of the pointwise ergodic theorem and Shannon-McMillan-Breiman theorem for discrete amenable groups, along Følner sequences that obey some restrictions. These restrictions are mild enough so that such sequences exist for all amenable groups.


References [Enhancements On Off] (What's this?)

  • 1. A. P. Calderon, A general ergodic theorem, Annals of Mathematics 58 (1953), no. 1, 182-191. MR 14:1071a
  • 2. W. R. Emerson, The pointwise ergodic theorem for amenable groups, American Journal of Mathematics 96 (1974), no. 3, 472-478. MR 50:7403
  • 3. W. R. Emerson and F. P. Greenleaf, Groups structure and the pointwise ergodic theorem for connected amenable groups, Advances in Math. 14 (1974), 153-172. MR 52:5867
  • 4. A. del Junco and J. Rosenblatt, Counterexamples in ergodic theory and number theory, Math. Ann. 245 (1979), 185-197. MR 81d:10042
  • 5. D. Ornstein and B. Weiss, The Shannon-McMillan-Breiman theorem for a class of amenable groups, Israel Journal of Mathematics 44 (1983), no. 1, 53-60. MR 85f:28018
  • 6. D. Ornstein and B. Weiss, The Shannon-McMillan-Breiman theorem for countable partitions, unpublished, c. 1985, 4 pages.
  • 7. D. Ornstein and B. Weiss, Entropy and isomorphism theorems for actions of amenable groups, Journal D'analyse Mathématique 48 (1987), 1-142. MR 88j:28014
  • 8. A. Paterson, Amenability, Mathematical Surveys and Monographs, vol. 29, American Mathematical Society, Providence, Rhode Island, 1988. MR 90e:43001
  • 9. D. Rudolph, Fundamentals of Measurable Dynamics - Ergodic theory on Lebesgue spaces, Oxford University Press, New York, 1990. MR 92e:28006
  • 10. A. Shulman, Maximal ergodic theorems on groups, Dep. Lit. NIINTI, No. 2184, 1988.
  • 11. A. Tempelman, Ergodic theorems for general dynamical systems, Dokl. Akad. Nauk SSSR 176 (1967), no. 4, 790-793; English translation: Soviet Math. Dokl. 8 (1967), no. 5, 1213-1216. MR 36:2779
  • 12. A. Tempelman, Ergodic theorems for group actions, informational and thermodynamical aspects, Kluwer Academic Publishers, Dordrecht, 1992. MR 94f:22007

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Additional Information

Elon Lindenstrauss
Affiliation: Institute of Mathematics, The Hebrew University, Jerusalem 91904, Israel
Email: elon@math.huji.ac.il

DOI: https://doi.org/10.1090/S1079-6762-99-00065-7
Keywords: Amenable groups, pointwise convergence, ergodic theorems
Received by editor(s): January 18, 1999
Published electronically: June 30, 1999
Additional Notes: The author would like to thank the Clore Foundation for its support.
Communicated by: Yitzhak Katznelson
Article copyright: © Copyright 1999 American Mathematical Society

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