Steven Kalikow

Twofold mixing implies threefold mixing for rank one transformations

This paper addresses the following long-standing open question: If a stationary transformation on a probability space obeys the property for all measurable sets A 1 , A 2 , does it follow that for all measurable sets A 1 , A 2 , A 3 ? Here we answer the question affirmatively for a certain class of transformations.

An Alpern tower independent of a given partition

Given a measure-preserving transformation

Infinite partitions and Rokhlin towers

T

Non-intersecting splitting ó-algebras in a non-Bernoulli transformation

of a probability space

Greedy is not so bad

(X, \mathcal B, \mu)

An outline of ergodic theory

and a finite measurable partition

Convergence properties in the nonhyperbolic case xn+1=xn−11+f(xn)

P

Random Markov processes for countable and uncountable alphabets

of

Random-step Markov processes

X

An Outline of Ergodic Theory: Ornstein isomorphism theorem

, we show how to construct an Alpern tower of any height whose base is independent of the partition