Orbit inequivalent actions of non-amenable groups
by Inessa Epstein
Abstract: We consider a Borel action of a countable group G on a standard Borel space X with a probability measure such that the action is free, ergodic and measure preserving. We may think of two such actions on spaces X and Y as being orbit equivalent if there is a Borel map witnessing that the actions are the same up to null sets. It is known that an amenable group admits only one free, ergodic, measure preserving Borel action up to
orbit equivalence. We show that a non-amenable group admits continuum many orbit inequivalent of this type.
For More Information: Greg Hjorth: G.Hjorth@ms.unimelb.edu.au