Centre for Discrete and Applicable Mathematics
	CDAM Research Report, LSE-CDAM-2005-21 December 2005

Towers, Conjugacy and Coding

Steve Alpern and V. S. Prasad

We consider three theorems in ergodic theory concerning a fixed aperiodic measure preserving transformation σ of a Lebesgue probability space (X, A, µ) and show that these theorems are all equivalent. Two of these results concern the existence of a partition of the space X with special properties. The third theorem asserts that the conjugates of σ are dense in the uniform topology on the space of automorphisms. The first partition result is Alpern’s generalization of the Rokhlin Lemma, the so-called Multiple Rokhlin Tower theorem stating that the space can be partitioned into denumerably many columns and the measures of the columns can be prescribed in advance; the second partition result is a coding result which asserts that any mixing Markov chain can be represented by σ and some partition of the space indexed by the state space of the Markov chain.

A PDF file (196 kB) with the full contents of this report can be downloaded by clicking here.

Alternatively, if you would like to get a free hard copy of this report, please send the number of this report, LSE-CDAM-2005-21, together with your name and postal address to:

		CDAM Research Reports Series Centre for Discrete and Applicable Mathematics London School of Economics Houghton Street London WC2A 2AE, U.K.
		Phone: +44(0)-20-7955 7494. Fax: +44(0)-20-7955 6877. Email: info@maths.lse.ac.uk

		Introduction to the CDAM Research Report Series.
		CDAM Homepage.

Last modified: 12th December 2005