An ergodic theorem for non-singular actions of the Heisenberg groups

Kieran Jarrett

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arXiv · 1702.04157

An ergodic theorem for non-singular actions of the Heisenberg groups

Kieran Jarrett

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Abstract

We show that there is a sequence of subsets of each discrete Heisenberg group for which the non-singular ergodic theorem holds. The sequence depends only on the group; it works for any of its non-singular 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 non-singular ergodic theorem. An exposition of how one proves non-singular ergodic theorems of this type is also included, along with a new proof for one of the key steps.

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Kieran Jarrett. 2017-02-14. An ergodic theorem for non-singular actions of the Heisenberg groups. https://arxiv.org/abs/1702.04157

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