a1 School of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia (email: firstname.lastname@example.org)
Mortiss introduced the notion of critical dimension of a non-singular action, a measure of the order of growth of sums of Radon derivatives. The critical dimension was shown to be an invariant of metric isomorphism; this invariant was calculated for two-point product odometers and shown to coincide, in certain cases, with the average coordinate entropy. In this paper we extend the theory to apply to all product odometers, introduce upper and lower critical dimensions, and prove a Katok-type covering lemma.
(Received December 14 2005)
(Revised July 08 2008)