An ergodic theorem for nonsingular actions of the Heisenberg groups
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- by Kieran Jarrett PDF
- Trans. Amer. Math. Soc. 372 (2019), 5507-5529 Request permission
Abstract:
We show that there is a sequence of subsets of each discrete Heisenberg group for which the nonsingular ergodic theorem holds. The sequence depends only on the group; it works for any of its nonsingular actions. To do this, we use a metric which was recently shown by Le Donne and Rigot to have the Besicovitch covering property and then apply an adaptation of Hochman’s proof of the multiparameter nonsingular ergodic theorem.References
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Additional Information
- Kieran Jarrett
- Affiliation: Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, United Kingdom
- Email: k.jarrett@bath.ac.uk
- Received by editor(s): March 23, 2017
- Received by editor(s) in revised form: June 13, 2018, and October 5, 2018
- Published electronically: January 16, 2019
- Additional Notes: The author thanks the University of Technology Sydney for their hospitality while much of the work was conducted.
- © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 372 (2019), 5507-5529
- MSC (2010): Primary 37A40, 37A30; Secondary 49Q15, 43A80
- DOI: https://doi.org/10.1090/tran/7750
- MathSciNet review: 4014285