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On measure transitive \(G\)-sets. (English) Zbl 1423.22021

Summary: In this paper, we consider measure preserving actions on abstract groups. By neglecting the null sets for a measure space, some properties of such an action can remain, but some of them will be dismissed. Our main goal is to determine the remaining properties as well as some measure properties of such actions. We also use such an action to create an action on \(L^1\).

MSC:

22F10 Measurable group actions
28D15 General groups of measure-preserving transformations
37A15 General groups of measure-preserving transformations and dynamical systems
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