TY - JOUR

T1 - Exchangeable measures for subshifts

AU - Aaronson, J.

AU - Nakada, H.

AU - Sarig, O.

N1 - Funding Information:
* Corresponding author. E-mail addresses: aaro@tau.ac.il (J. Aaronson), nakada@math.keio.ac.jp (H. Nakada), sarig@math.psu.edu (O. Sarig). 1 Tel.: +972 3 6408805; fax: +972 3 6409357. 2 Tel.: +81 45 566 1641; fax: +81 45 566 1642. 3 The third author acknowledges support of NSF grant DMS-0500630. Tel.: +1 814 8639678; fax: +1 814 8653735.

PY - 2006/11

Y1 - 2006/11

N2 - 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 ≠ 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).

AB - 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 ≠ 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).

KW - Beta expansions

KW - Countable Markov shifts

KW - Exchangeability

KW - Tail equivalence relations

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U2 - 10.1016/j.anihpb.2005.10.002

DO - 10.1016/j.anihpb.2005.10.002

M3 - Article

AN - SCOPUS:33750194099

VL - 42

SP - 727

EP - 751

JO - Annales de l'institut Henri Poincare (B) Probability and Statistics

JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

SN - 0246-0203

IS - 6

ER -