We call an ergodic measure-preserving action of a locally compact group G on a probability space simple if every ergodic joining of it to itself is either product measure or is supported on a graph, and a similar condition holds for multiple self-joinings. This generalizes Rudolph's notion of minimal self-joinings and Veech's property S.
Main results The joinings of a simple action with an arbitrary ergodic action can be explicitly descnbed. A weakly mixing group extension of an action with minimal self-joinings is simple. The action of a closed, normal, co-compact subgroup in a weakly-mixing simple action is again simple. Some corollaries. Two simple actions with no common factors are disjoint. The time-one map of a weakly mixing flow with minimal self-joinings is prime Distinct positive times in a -action with minimal self-joinings are disjoint.
Email your librarian or administrator to recommend adding this journal to your organisation's collection.
* Views captured on Cambridge Core between September 2016 - 27th May 2017. This data will be updated every 24 hours.