Geometry of Sets and Measures in Euclidean Spaces - Fractals and Rectifiability

Inhaltsverzeichnis

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.

Zusammenfassung

Now in paperback, the main theme of this book is the study of geometric properties of general sets and measures in euclidean space. Examples to which this theory applies include fractal-type objects such as strange attractors for dynamical systems, and those fractals used as models in the sciences.

Produktdetails

• Autoren: Pertti Mattila, Pertti (University of Jyvaskyla Mattila
• Mitarbeit: Bela Bollobas (Herausgeber), W. Fulton (Herausgeber)
• Verlag: Cambridge University Press ELT
• Sprache: Englisch
• Produktform: Taschenbuch
• Erschienen: 25.02.1999
• EAN: 9780521655958
• ISBN: 978-0-521-65595-8
• Seiten: 356
• Serien: Cambridge Studies in Advanced Mathematics; Cambridge Studies in Advanced; Cambridge Studies in Advanced Mathematics
• Thema: Naturwissenschaften, Medizin, Informatik, Technik > Mathematik > Sonstiges