2017/02/14 by Kieran Jarrett, Jarrett, Kieran
Mathematics · #37A40 (Primary) 37A30 #43A80 (Secondary) #49Q15 #Advanced Harmonic Analysis Research #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Metric Geometry (math.MG) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1702.04157
openalex publication_date 2017/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.