Seminar 6.1.17 Moreira

Title: Quasi-disjointness

SpeakerJoel Moreira (Northwestern University)

Abstract: The Kronecker factor of a measure preserving system is the factor generated by all the almost periodic functions and has an explicit algebraic description. A surprising result of Berg essentially classifies the joinings of two ergodic measure preserving Z-systems in terms of the joinings of their Kronecker factors (which have an easy algebraic description), if one of the systems is (measurable) distal. Using Berg’s terminology, he showed that any ergodic Z-system is quasidisjoint. from any ergodic distal Z-system. In this talk I will explore the notion of quasidisjointness, and present an alternative definition of quasidisjointness which makes sense for measure preserving actions of any group and agrees with Berg’s definition for Z actions.