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 α √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.
Original language | English |
---|---|
Pages (from-to) | 1-21 |
Number of pages | 21 |
Journal | Fundamenta Mathematicae |
Volume | 206 |
Issue number | 1 |
DOIs | |
State | Published - 2009 |
Keywords
- Conservative
- Entropy
- Entropy dimension
- Ergodic
- Measure preserving transformation
- Predictable set
- Quasifinite