Ergodic Theory and Dynamical Systems

Research Article

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

A. H. DOOLEYa1 and DANIEL J. RUDOLPHa1

a1 School of Mathematics, University of New South Wales, Sydney 2052, Australia (email: a.dooley@unsw.edu.au)

Abstract

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.

(Received December 09 2010)

(Revised May 06 2011)

(Online publication September 16 2011)

Footnotes

† (1949–2010).

Dedicated to the memory of Daniel Rudolph