Exchangeable measures for subshifts |
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| Authors: | J Aaronson H Nakada O Sarig |
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| Institution: | aSchool of Math. Sciences, Tel Aviv University, 69978 Tel Aviv, Israel;bDept. of Math., Keio University, Hiyoshi 3-14-1 Kohoku, Yokohama 223, Japan;cDept. of Math., Penn State University, University Park, PA 16802, USA |
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| Abstract: | Let Ω be a Borel subset of  where S is countable. A measure is called exchangeable on Ω, if it is supported on Ω and is invariant under every Borel automorphism of Ω which permutes at most finitely many coordinates. De-Finetti's theorem characterizes these measures when  . We apply the ergodic theory of equivalence relations to study the case  , and obtain versions of this theorem when Ω is a countable state Markov shift, and when Ω is the collection of beta expansions of real numbers in 0,1] (a non-Markovian constraint). |
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| Keywords: | Exchangeability Tail equivalence relations Beta expansions Countable Markov shifts |
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