Generic distributional limits for measure preserving transformations
type: Item
instance of: scholarly article
title: Generic distributional limits for measure preserving transformations
zbMATH Open document ID: 0539.28009
DOI: 10.1007/BF02760521
author: Benjamin Weiss
author: Jon Aaronson
published in: Israel Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: We construct a conservative ergodic measure preserving transformation of the real line \(({\mathbb{R}},{\mathbb{B}},m,T)\) whose Birkhoff sums are distributionally generic in the following sense: For every random variable Y on \([0,\infty]\) there are constants \(a_ n>0\) and a subsequence \(n_ k\to \infty\) so that \[ P-dist.(1/a_{n_ k})\sum^{n_ k}_{j=1}f{\mathbb{O}}T^ j\to dist.Y\int_{{\mathbb{R}}}fdm \] for every m-absolutely continuous probability P, and non-negative integrable function f.
Mathematics Subject Classification ID: 28D10
Mathematics Subject Classification ID: 28D05
zbMATH DE Number: 3857425
zbMATH Keywords: conservative ergodic measure preserving transformation
zbMATH Keywords: Birkhoff sums
zbMATH Keywords: distributionally generic
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3857425