Exchangeable Measures for Subshifts
نویسندگان
چکیده
Let Ω be a Borel subset of SN 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 Ω = SN. We apply the ergodic theory of equivalence relations to study the case Ω 6= SN, 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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