Exchangeable measures for subshifts

Details Exchangeable measures for subshifts Exchangeable measures for subshifts

2004-06-28

arxiv.org/abs/math/0406578v4

Ann. Inst. H. Poincar\'e Probab. Statist. 42 (2006), no. 6, 727--751

Mathematics

Dynamical Systems

Scientific paper

Let $\Om$ be a Borel subset of $S^\Bbb N$ where $S$ is countable. A measure is called exchangeable on $\Om$, if it is supported on $\Om$ and is invariant under every Borel automorphism of $\Om$ which permutes at most finitely many coordinates. De-Finetti's theorem characterizes these measures when $\Om=S^\Bbb N$. We apply the ergodic theory of equivalence relations to study the case $\Om\neq S^\Bbb N$, and obtain versions of this theorem when $\Om$ is a countable state Markov shift, and when $\Om$ is the collection of beta expansions of real numbers in $[0,1]$ (a non-Markovian constraint).

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