## LSU Historical Dissertations and Theses

1988

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

Mathematics

Raymond C. Fabec

#### Abstract

We describe ergodic Borel actions of a semi-direct product group $K$ $\times\sb{s}$ $G$ on a standard Borel space where G is a group acting on a compact group K by automorphisms. In the canonical action of G on the dual K of K we assume each G-orbit in K is finite. This condition is automatically satisfied if K is a compact connected semi-simple Lie group. We discuss amenable actions and relatively weakly-mixing actions of this semi-direct product group.

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