Abstract and Applied Analysis
Volume 2006 (2006), Article ID 81356, 15 pages
doi:10.1155/AAA/2006/81356
Dynamics via measurability
Department of Mathematics, University of Illinois at Urbana, Urbana 61801, IL, USA
Received 4 February 2005; Accepted 21 March 2005
Copyright © 2006 Svetlana Butler and Joseph Rosenblatt. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Generators f for σ-algebras can be used to view the
dynamics of an invertible measurable transformation T in terms
of the range values of f∘T. Such generators are the norm
rather than the exception. Related measurable and quantitative
methods of estimating a function from the behavior of ergodic
averages are also discussed.