Zum invarianten Inhalt und Maß in topologischen Räumen (Q2266775)

Let R be a topological space and G a transformation group on R. The ordered pair (R,G) is called Klein space. We start with the concept of decomposition of certain compact sets X which are assumed to have the topological property \(X=cl int X.\) Contrary to the classic measure theory it is only required that the decomposition sets have no common interior points. Conditions for existence and uniqueness of G-invariant contents are formulated and proved with the help of algebraic methods. If an additional axiom is satisfied this contents are premeasures, i.e. the Klein space (R,G) can be equipped with a G-invariant measure.