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The focus of this book is 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 for the subject and develops all the main tools used in its study, 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 Besicovitch-Federer theory of rectifiable sets, which form in a sense the largest class of subsets of Euclidean space possessing many of the properties of smooth surfaces.Read more
- Geometric measure theory is a subject now in vogue
- Author is an authority in the field
- Explains the analytical mathematics behind fractals
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"Provides a unified theory for the study of the topic and develops the main tools used in its study including theorems, Hausdorff measures, and their relations to Riesz capacities and Fourier transforms." Book News, Inc.
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- Date Published: March 1999
- format: Paperback
- isbn: 9780521655958
- length: 356 pages
- dimensions: 226 x 152 x 23 mm
- weight: 0.52kg
- availability: Available
Table of Contents
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
List of notation
Index of terminology.
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