Point Transitive Transformation Groups

Let T be an abstract group, (beta T, T) the betac mpactificati n of T regarded as a transformation group with phase group T. The collection of all point transitive transformati n groups (X, T) with compact phase space X is studied by representing each such X as a set of homomorphisms of certain subalgebras of C(beta T) into C(beta T). (Author).

This book is devoted to some topics of the general theory of invariant and quasi-invariant measures. Such measures are usually defined on various sigma-algebras of subsets of spaces equipped with transformation groups, and there are close relationships between purely algebraic properties of these groups and the corresponding properties of invariant (quasi-invariant) measures. The main goal of the book is to investigate several aspects of those relationships (primarily from the set-theoretical point of view). Also of interest are the properties of some natural classes of sets, important from the viewpoint of the theory of invariant (quasi-invariant) measures.