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Non-uniqueness in -measures

  • A. H. DOOLEY (a1) and DANIEL J. RUDOLPH (a1)

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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[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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