Borel transversals and ergodic measures on indecomposable continua
The Effros theorem on the polonais transformation group has already had nice applications in the theory of homogeneous continua. Now the idea of Effros is applied to indecomposable continua and its decomposition into composants. The Borel structure of this quotient space, the existence of ergodic measures, Borel transversals and Borel cross-sections are investigated, and some relationships are proved. The case of solenoids and Knaster continua is studied in detail - the solenoids because of the existence of an \({\mathbb{R}}\)-action on it such that orbits are precisely the composants, and the Knaster continuum is the image of some solenoid under an appropriate map. Many references are given.
scientific article; zbMATH DE number 3975859
scientific article