J. Austral. Math. Soc.  73 (2002), 171-186
Average co-ordinate entropy

Genevieve Mortiss
  School of Mathematics
  The University of New South Wales
  Sydney NSW 2052
  Australia
  mortiss@maths.unsw.edu.au


Abstract
A notion of entropy for the non-singular action of finite co-ordinate changes on $\big(X=\prod_{i=1}^{\infty}\mathbb{Z}_2,\mu\big)$ is introduced. This quantity---average co-ordinate or AC entropy---is calculated for product measures and  G-measures. It is shown that the type III classes can be subdivided using AC entropy. An equivalence relation is established for which AC entropy is an invariant.
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