Borel transversals and ergodic measures on indecomposable continua
type: Item
instance of: scholarly article
title: Borel transversals and ergodic measures on indecomposable continua
zbMATH Open document ID: 0604.54032
DOI: 10.1016/0166-8641(86)90065-9
author: James T. jun. Rogers
published in: Topology and its Applications
publication date: 1986-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 54F15
Mathematics Subject Classification ID: 28C15
zbMATH DE Number: 3975859
zbMATH Keywords: Effros theorem
zbMATH Keywords: polonais transformation group
zbMATH Keywords: indecomposable continua
zbMATH Keywords: Borel structure
zbMATH Keywords: quotient space
zbMATH Keywords: ergodic measures
zbMATH Keywords: Borel transversals
zbMATH Keywords: Borel cross-sections
zbMATH Keywords: solenoids
zbMATH Keywords: Knaster continua
MaRDI profile type: Publication
full work available at URL: 0166-8641(86)90065-9
OpenAlex ID: W1979182440
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description: scientific article; zbMATH DE number 3975859