We show that a certain type of quasi finite, 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 quasi finite; and consider distribution asymptotics of information showing that e.g. for Boole’s transformation, information is as...

We show that a certain type of quasi finite, 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 quasi finite; and consider distribution asymptotics of information showing that e.g. for Boole’s transformation, information is as...