Infinite measure~preserving~transformations with Radon MSJ

2015/03/05 by Danilenko, Alexandre I.
#37A15 #37A35 #37A40 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1503.01568

Abstract

We introduce concepts of Radon MSJ and Radon disjointness for infinite Radon measure preserving homeomorphisms of the locally compact Cantor space. We construct an uncountable family of pairwise Radon disjoint infinite Chacon like transformations. Every such transformation is Radon strictly ergodic, totally ergodic, asymmetric (not isomorphic to its inverse), has Radon MSJ and possesses Radon joinings whose ergodic components are not joinings.

Related

• Nearly finite Chacon Transformation
• Uniform sets for infinite measure-preserving systems
• Chacon's Type Ergodic Transformations with Unbounded Arithmetic Spacers
• Oscillating and nonsummable Radon-Nikodym cocycles along the forward geodesic of measure-class-preserving transformations
• Sets of full measure avoiding Cantor sets