Geometry of Sets and Measures in Euclidean Spaces
Fractals and Rectifiability
Part of Cambridge Studies in Advanced Mathematics
- Author: Pertti Mattila, University of Jyväskylä, Finland
- Date Published: February 1999
- availability: Available
- format: Paperback
- isbn: 9780521655958
Paperback
Other available formats:
eBook
Looking for an inspection copy?
This title is not currently available on inspection
-
Now in paperback, the main theme of this book is the study of geometric properties of general sets and measures in euclidean spaces. Applications of this theory include fractal-type objects such as strange attractors for dynamical systems and those fractals used as models in the sciences. The author provides a firm and unified foundation and develops all the necessary main tools, such as covering theorems, Hausdorff measures and their relations to Riesz capacities and Fourier transforms. The last third of the book is devoted to the Beisovich-Federer theory of rectifiable sets, which form in a sense the largest class of subsets of euclidean space posessing many of the properties of smooth surfaces. These sets have wide application including the higher-dimensional calculus of variations. Their relations to complex analysis and singular integrals are also studied. Essentially self-contained, this book is suitable for graduate students and researchers in mathematics.
Read more- Geometric measure theory is a subject now in vogue
- Author is an authority in the field
- Explains the analytical mathematics behind fractals
Customer reviews
Not yet reviewed
Be the first to review
Review was not posted due to profanity
×Product details
- Date Published: February 1999
- format: Paperback
- isbn: 9780521655958
- length: 356 pages
- dimensions: 226 x 152 x 23 mm
- weight: 0.52kg
- availability: Available
Table of Contents
Acknowledgements
Basic notation
Introduction
1. General measure theory
2. Covering and differentiation
3. Invariant measures
4. Hausdorff measures and dimension
5. Other measures and dimensions
6. Density theorems for Hausdorff and packing measures
7. Lipschitz maps
8. Energies, capacities and subsets of finite measure
9. Orthogonal projections
10. Intersections with planes
11. Local structure of s-dimensional sets and measures
12. The Fourier transform and its applications
13. Intersections of general sets
14. Tangent measures and densities
15. Rectifiable sets and approximate tangent planes
16. Rectifiability, weak linear approximation and tangent measures
17. Rectifiability and densities
18. Rectifiability and orthogonal projections
19. Rectifiability and othogonal projections
19. Rectifiability and analytic capacity in the complex plane
20. Rectifiability and singular intervals
References
List of notation
Index of terminology.
Sorry, this resource is locked
Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org
Register Sign in» Proceed
You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.
Continue ×Are you sure you want to delete your account?
This cannot be undone.
Thank you for your feedback which will help us improve our service.
If you requested a response, we will make sure to get back to you shortly.
×