jgpropp@athena.mit.edu (James Propp) (10/24/90)
Suppose X is a 2-dimensional shift of finite type. Must there exist a translation-invariant measure on X that gives every open set a well-defined Banach density? (That is: does there exist an invariant measure m such that any invariant measure that is singular with respect to m has support not intersecting that of m?) My guess is "no". Perhaps someone can point me to an example of a 2- dimensional SFT that is topologically minimal but not uniquely ergodic (since that would be the simplest sort of counter-example). Jim Propp (propp@math.mit.edu)