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-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-23T02:38:19.977Z Has data issue: false hasContentIssue false

4 - Dimensions of Measures

from Part One - Theory

Published online by Cambridge University Press:  13 October 2020

Jonathan M. Fraser
Jonathan M. Fraser
Affiliation:
University of St Andrews, Scotland
Get access

Summary

A key aspect of dimension theory is how dimensions of sets relate to dimensions of measures. To this end, all the familiar notions of dimension for sets have natural counterparts in the context of measures. The Assouad dimension and its many variants are no different and in this chapter we explore the dimensions and spectra of measures.

Keywords

Assouad spectrumquasi-Assouad dimensionlower dimensionlower spectrum
Type
Chapter
Information
Assouad Dimension and Fractal Geometry , pp. 56 - 63
Publisher: Cambridge University Press
Print publication year: 2020

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.

  • Dimensions of Measures
  • Jonathan M. Fraser, University of St Andrews, Scotland
  • Book: Assouad Dimension and Fractal Geometry
  • Online publication: 13 October 2020
  • Chapter DOI: https://doi.org/10.1017/9781108778459.005
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.

  • Dimensions of Measures
  • Jonathan M. Fraser, University of St Andrews, Scotland
  • Book: Assouad Dimension and Fractal Geometry
  • Online publication: 13 October 2020
  • Chapter DOI: https://doi.org/10.1017/9781108778459.005
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.

  • Dimensions of Measures
  • Jonathan M. Fraser, University of St Andrews, Scotland
  • Book: Assouad Dimension and Fractal Geometry
  • Online publication: 13 October 2020
  • Chapter DOI: https://doi.org/10.1017/9781108778459.005
Available formats
×