Predictability, entropy and information of infinite transformations
Volume 206 / 2009
Fundamenta Mathematicae 206 (2009), 1-21
MSC: 37A40, 60F05.
DOI: 10.4064/fm206-0-1
Abstract
We show that a certain type of quasifinite, conservative, ergodic, measure preserving transformation always has a maximal zero entropy factor, generated by predictable sets. We also construct a conservative, ergodic, measure preserving transformation which is not quasifinite; and consider distribution asymptotics of information showing that e.g. for Boole's transformation, information is asymptotically mod-normal with normalization $\propto\sqrt n$. Lastly, we show that certain ergodic, probability preserving transformations with zero entropy have analogous properties and consequently entropy dimension of at most $1/2$.
