Ebook: Introduction to Ergodic Theory

These notes originally formed part of a course given at the
University of New Mexico in the spring of 1967. They were later
revised during a course given in the spring of 1968 while the au-
thor was a visiting lecturer at Westfield College, University of
London. The topics that are discussed concern problems in er-
godic theory related to point transformations in a measure space.
A basic course in measure theory is assumed. For a few results
we refer to the monograph Lectures on Ergodic Theory by
P. R. Halmos, hereafter referred to as [H].

Contents:

Preface


.... .. . ... ......... ... .. .. ... .... ..... .


i


1. Point Transformations ........................ 1
2. Ergodic Theorem ............................ 19
3. Finite Invariant Measures ..... ................. 31
4. Sigma-Finite Invariant Measures ............... 47
s. Mixing Transformations ..... p . . . . . . . . . . . . . . . .. 61
6. Stacking Method ............................. 75
7. Uniform Approximation .............. . . . . . . . . . 101
8. Roots of Transformations . . . . . . . . . . . . . . . . . . . .. 115
9. Induced Transformations ...................... 125
Remarks .................................... 133
Bibliography.. . . . . .. . . . . .. . . . . . . . . . . . .. . . ... 137