# Ergodic Theorems for Group Actions

- Author : A.A. Tempelman
- Publsiher : Springer Science & Business Media
- Release : 17 April 2013
- ISBN : 9789401714600
- Page : 399 pages
- Rating : 4/5 from 21 voters

Download or read online book entitled Ergodic Theorems for Group Actions written by A.A. Tempelman and published by Springer Science & Business Media. This book was released on 17 April 2013 with total page 399 pages. Available in PDF, EPUB and Kindle. Get best books that you want by click Get Book Button and Read as many books as you like. Book Excerpt : This volume is devoted to generalizations of the classical Birkhoff and von Neuman ergodic theorems to semigroup representations in Banach spaces, semigroup actions in measure spaces, homogeneous random fields and random measures on homogeneous spaces. The ergodicity, mixing and quasimixing of semigroup actions and homogeneous random fields are considered as well. In particular homogeneous spaces, on which all homogeneous random fields are quasimixing are introduced and studied (the n-dimensional Euclidean and Lobachevsky spaces with n>=2, and all simple Lie groups with finite centre are examples of such spaces. Also dealt with are applications of general ergodic theorems for the construction of specific informational and thermodynamical characteristics of homogeneous random fields on amenable groups and for proving general versions of the McMillan, Breiman and Lee-Yang theorems. A variational principle which characterizes the Gibbsian homogeneous random fields in terms of the specific free energy is also proved. The book has eight chapters, a number of appendices and a substantial list of references. For researchers whose works involves probability theory, ergodic theory, harmonic analysis, measure theory and statistical Physics.