Infinite measure~preserving~transformations with Radon MSJ

TL;DR

This paper introduces Radon MSJ and disjointness for infinite Radon measure preserving homeomorphisms, constructing uncountably many Radon disjoint transformations with unique ergodic and mixing properties.

Contribution

It develops new concepts of Radon MSJ and disjointness and constructs a large family of Radon disjoint transformations with novel ergodic characteristics.

Findings

Uncountable family of Radon disjoint transformations

Transformations are Radon strictly ergodic and totally ergodic

Transformations are asymmetric with unique Radon joinings

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.