 9922 J. Schmeling and S. Troubetzkoy
 Entropy regular sets
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Jan 21, 99

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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.
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