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- Title
A ratio ergodic theorem for commuting, conservative, invertible transformations with quasi-invariant measure summed over symmetric hypercubes.
- Authors
JACOB FELDMAN
- Abstract
Let $T(1),\dots,T(d)$ be conservative, invertible, non-singular, commuting transformations on the Polish measure space $(X,m)$. Then for $f$ and $p$ in $L^1(m)$ with $p>0$,\[\frac{{\hat T}(1)_{-N}^N \dotsb {\hat T}(d)_{-N}^Nf}{{\hat T}(1)_{-N}^N \dotsb {\hat T}(d)_{-N}^Np}\to E[f | {\mathcal I}]/E[p| {\mathcal I}]\quad \text{as }N\to\infty.\]
- Subjects
ERGODIC theory; CONTINUOUS groups; MATHEMATICAL physics; MATHEMATICAL transformations; ALGORITHMS
- Publication
Ergodic Theory & Dynamical Systems, 2007, Vol 27, Issue 4, p1135
- ISSN
0143-3857
- Publication type
Article
- DOI
10.1017/S0143385707000119