Introduction to Ergodic Theory

Description

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