# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Predictability, entropy and information of infinite transformations

### Tom 206 / 2009

Fundamenta Mathematicae 206 (2009), 1-21 MSC: 37A40, 60F05. DOI: 10.4064/fm206-0-1

#### Streszczenie

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 $1/2$.

#### Autorzy

• Jon AaronsonSchool of Math. Sciences
Tel Aviv University
69978 Tel Aviv, Israel
e-mail
• Kyewon Koh ParkDepartment of Mathematics
Ajou University
Suwon 442-729, South Korea
e-mail

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