Geometry of sets and measures in Euclidean spaces fractals and rectifiability

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.