Abstract
An ergodic Zd-action α by automorphisms of a compact, abelian group X usually has many distinct non-atomic, invariant, ergodic probability measures. For example, if d ≥ 1, and if α is the shift-action (2.1) of Zd on X = G Z 2 , where G is a nontrivial, compact, abelian group, then there exist uncountably many distinct, a-invariant, mixing probability measures on X:
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Basel AG
About this chapter
Cite this chapter
Schmidt, K. (1995). CHAPTER IX Rigidity. In: Dynamical Systems of Algebraic Origin. Modern Birkhäuser Classics. Springer, Basel. https://doi.org/10.1007/978-3-0348-0277-2_9
Download citation
DOI: https://doi.org/10.1007/978-3-0348-0277-2_9
Published:
Publisher Name: Springer, Basel
Print ISBN: 978-3-0348-0276-5
Online ISBN: 978-3-0348-0277-2
eBook Packages: Springer Book Archive