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- Title
The critical dimension for $G$-measures.
- Authors
MANSFIELD, DANIEL F.; DOOLEY, ANTHONY H.
- Abstract
The critical dimension of an ergodic non-singular dynamical system is the asymptotic growth rate of sums of consecutive Radon–Nikodým derivatives. This has been shown to equal the average coordinate entropy for product odometers when the size of individual factors is bounded. We extend this result to $G$-measures with an asymptotic bound on the size of individual factors. Furthermore, unlike von Neumann–Krieger type, the critical dimension is an invariant property on the class of ergodic $G$-measures.
- Publication
Ergodic Theory & Dynamical Systems, 2017, Vol 37, Issue 3, p824
- ISSN
0143-3857
- Publication type
Article
- DOI
10.1017/etds.2015.69