Predictability, entropy and information of infinite transformations

• Autorzy: Jon Aaronson , Kyewon Koh Park
• Języki publikacji: EN

Abstrakty

EN

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 ∝ √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.

Kategorie tematyczne

• 37A40: Nonsingular (and infinite-measure preserving) transformations
• 60F05: Central limit and other weak theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2009
• Tom: 206
• Numer: 1
• Strony: 1-21

Daty

wydano

2009

Twórcy

autor

Jon Aaronson

• School of Math. Sciences, Tel Aviv University, 69978 Tel Aviv, Israel

autor

Kyewon Koh Park

• Department of Mathematics, Ajou University, Suwon 442-729, South Korea

Identyfikatory

DOI

10.4064/fm206-0-1