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Tony Dooley

University of New South Wales


In the late 1970s, Gavin observed that Riesz product measures based on powers of 3 are ergodic for the action of the triadic rationals. This caused us to examine the role of Riesz product type constructions in ergodic theory and led us to explore the theory of G-measures.

I will give an overview of our work, and show how it has now led to a structure theorem for all non-singular ergodic dynamical systems up to orbit equivalence: Hamachi and I recently proved that every such system is orbit equivalent to a uniquely ergodic G-measure on a Bratteli-Vershik space, realised as an induced transformation on a closed set of an infinite product space.