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Abstract and Applied Analysis
Volume 2006, Article ID 81356, 15 pages

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.


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 fT. 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.