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    MANSFIELD, DANIEL F. and DOOLEY, ANTHONY H. 2015. The critical dimension for -measures. Ergodic Theory and Dynamical Systems, p. 1.


Non-uniqueness in -measures

  • A. H. DOOLEY (a1) and DANIEL J. RUDOLPH (a1)
  • DOI:
  • Published online: 16 September 2011

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.

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[4]G. Brown and A. H. Dooley . Dichotomy theorems for G-measures. Int. J. Math. 5 (1994), 827834.

[5]G. Brown and A. H. Dooley . On G-measures and product measures. Ergod. Th. & Dynam. Sys. 18 (1998), 95107.

[7]M. Bramson and S. Kalikow . Nonuniqueness in g-functions. Israel J. Math. 84 (1993), 153160.

[9]A. H. Dooley and T. Hamachi . Non-singular dynamical systems, Bratteli diagrams and Markov odometers. Israel J. Math. 138 (2003), 93123.

[11]H. Dye . On groups of measure-preserving transformations I. Amer. J. Math. 81 (1959), 119159.

[13]M. Keane . Strongly mixing g-measures. Invent. Math. 16 (1972), 309324.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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