Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!yale!mintaka!bloom-beacon!daemon
From: jgpropp@athena.mit.edu (James Propp)
Newsgroups: comp.theory.dynamic-sys
Subject: invariant measures for 2-dimensional SFT's
Message-ID: <1990Oct23.170317.11670@athena.mit.edu>
Date: 23 Oct 90 17:03:17 GMT
Sender: daemon@athena.mit.edu (Mr Background)
Organization: Massachusetts Institute of Technology
Lines: 11

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)