J. Schmeling and S. Troubetzkoy
Entropy regular sets
(60K, dvi file)

ABSTRACT.  One of the objects of geometric measure theory is to derive global 
geometric structures from local properties (densities with respect to the 
$s$--dimensional Hausdorff measure). In the framework of 
dynamical system it 
is more natural to consider entropy measures instead of Hausdorff 
measures. Our aim is to show that {\em regular} subshifts 
(with respect to the entropy measure) necessarily have a special rigid 
structure. Moreover, their entropy has to be the logarithm of an 
integer. This parallels the well known fact that regular sets 
(with respect to the Hausdorff measure) have to have integral dimension.