Abstract
We introduce the notion of a joining between two measure-preserving systems, and develop the basic properties of joinings. The tools developed in Chapter 5 are used to give a different purely measure-theoretic approach to the ergodic decomposition and to give a construction of the Kronecker factor of a measure-preserving system. The classification of Kronecker systems due to Halmos and von Neumann is proved.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer-Verlag London Limited
About this chapter
Cite this chapter
Einsiedler, M., Ward, T. (2011). Factors and Joinings. In: Ergodic Theory., vol 259. Springer, London. https://doi.org/10.1007/978-0-85729-021-2_6
Download citation
DOI: https://doi.org/10.1007/978-0-85729-021-2_6
Publisher Name: Springer, London
Print ISBN: 978-0-85729-020-5
Online ISBN: 978-0-85729-021-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)