Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- Part One Theory
- 1 Fractal Geometry and Dimension Theory
- 2 The Assouad Dimension
- 3 Some Variations on the Assouad Dimension
- 4 Dimensions of Measures
- 5 Weak Tangents and Microsets
- Part Two Examples
- Part Three Applications
- References
- List of Notation
- Index
4 - Dimensions of Measures
from Part One - Theory
Published online by Cambridge University Press: 13 October 2020
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- Part One Theory
- 1 Fractal Geometry and Dimension Theory
- 2 The Assouad Dimension
- 3 Some Variations on the Assouad Dimension
- 4 Dimensions of Measures
- 5 Weak Tangents and Microsets
- Part Two Examples
- Part Three Applications
- References
- List of Notation
- Index
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.
- Type
- Chapter
- Information
- Assouad Dimension and Fractal Geometry , pp. 56 - 63Publisher: Cambridge University PressPrint publication year: 2020