Generic distributional limits for measure preserving transformations
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.
conservative ergodic measure preserving transformation
scientific article; zbMATH DE number 3857425