Predictability, entropy and information of infinite transformations

Jon Aaronson, and Kyewon Koh Park. "Predictability, entropy and information of infinite transformations." Fundamenta Mathematicae 206.1 (2009): 1-21. <http://eudml.org/doc/282870>.

@article{JonAaronson2009,
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 ∝ √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.},
author = {Jon Aaronson, Kyewon Koh Park},
journal = {Fundamenta Mathematicae},
keywords = {measure preserving transformation; conservative; ergodic; entropy; quasifinite; predictable set; entropy dimension},
language = {eng},
number = {1},
pages = {1-21},
title = {Predictability, entropy and information of infinite transformations},
url = {http://eudml.org/doc/282870},
volume = {206},
year = {2009},
}

TY - JOUR
AU - Jon Aaronson
AU - Kyewon Koh Park
TI - Predictability, entropy and information of infinite transformations
JO - Fundamenta Mathematicae
PY - 2009
VL - 206
IS - 1
SP - 1
EP - 21
AB - 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.
LA - eng
KW - measure preserving transformation; conservative; ergodic; entropy; quasifinite; predictable set; entropy dimension
UR - http://eudml.org/doc/282870
ER -