## Isometry groups of Borel randomizations.(English)Zbl 1484.03090

Summary: We study global dynamical properties of the isometry group of the Borel randomization of a separable complete structure. We show that if properties such as the Rokhlin property, topometric generics, and extreme amenability hold for the isometry group of the structure, then they also hold in the isometry group of the randomization.

### MSC:

 03E15 Descriptive set theory 54H11 Topological groups (topological aspects) 22F50 Groups as automorphisms of other structures 22A05 Structure of general topological groups
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### References:

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