Non-uniqueness in $\boldsymbol {G}$-measures

Bramson and Kalikow and Quas showed the phenomenon of non-uniqueness for g-measures in the absence of a C1 condition on g. We extend this result to show that for a sequence G=(Gn), the class of G-measures can be badly behaved in the sense of containing measures of type IIIλ for all λ in a continuous...

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Bibliographic Details
Published in:Ergodic theory and dynamical systems 2012-04, Vol.32 (2), p.575-586
Main Authors: DOOLEY, A. H., RUDOLPH, DANIEL J.
Format: Article
Language:English
Subjects:
Dynamical systems
Ergodic processes
Online Access:Get full text
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Summary:Bramson and Kalikow and Quas showed the phenomenon of non-uniqueness for g-measures in the absence of a C1 condition on g. We extend this result to show that for a sequence G=(Gn), the class of G-measures can be badly behaved in the sense of containing measures of type IIIλ for all λ in a continuous image of an Fσ set.
ISSN:0143-3857
1469-4417
DOI:10.1017/S0143385711000423