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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

An ergodic theorem for nonsingular actions of the Heisenberg groups


Author: Kieran Jarrett
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 37A40, 37A30; Secondary 49Q15, 43A80
DOI: https://doi.org/10.1090/tran/7750
Published electronically: January 16, 2019
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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.


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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

DOI: https://doi.org/10.1090/tran/7750
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.
Article copyright: © Copyright 2019 American Mathematical Society