Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-19T05:29:00.853Z Has data issue: false hasContentIssue false

2 - Invariant Measures: Finite and Infinite

from Part I - Ergodic Theory and Geometric Measures

Published online by Cambridge University Press:  20 April 2023

Janina Kotus  and
Mariusz Urbański
Janina Kotus
Affiliation:
Warsaw University of Technology
Mariusz Urbański
Affiliation:
University of North Texas
Get access

Summary

We prove in this chapter the Bogolyubov-Krylov Theorem about the existence of Borel probability invariant measures for continuous dynamical systems acting on compact metrizable topological spaces. We also establish in this chapter the basic properties of invariant and ergodic measures and provide several examples of such measures.

Keywords

Bogolyubov–Krylov Theoremexamples of invariant and ergodic measures
Type
Chapter
Information
Meromorphic Dynamics
Abstract Ergodic Theory, Geometry, Graph Directed Markov Systems, and Conformal Measures
 , pp. 55 - 101
Publisher: Cambridge University Press
Print publication year: 2023

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×