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Book Review

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Book Information:

Author: Pertti Mattila
Title: Geometry of sets and measures in Euclidean spaces
Additional book information: Cambridge Studies in Advanced Mathematics, vol. 44, Cambridge University Press, 1995, x+343 pp., ISBN 0-521-46576-1, $49.95

References [Enhancements On Off] (What's this?)

  • 1. M. Barnsley, Fractals Everywhere, Academic Press, 1988. MR 90e:58080
  • 2. L. Carleson, Selected Problems on Exceptional Sets, van Nostrand, 1967. MR 37:1576
  • 3. G.A. Edgar, Measure, Topology, and Fractal Geometry, Springer, 1990. MR 92a:54001
  • 4. K.J. Falconer, The Geometry of Fractal Sets, Cambridge University Press, 1985. MR 88d:28001
  • 5. K.J. Falconer, Fractal Geometry: Mathematical Foundations and Applications, Wiley, 1990. MR 92j:28008
  • 6. H. Federer, Geometric Measure Theory, Springer, 1969, reprinted 1996. MR 41:1976
  • 7. H. Federer, Colloquium lectures in geometric measure theory, Bull. Amer. Math. Soc. 84 (1978), 291-338. MR 57:7330
  • 8. R.M. Hardt, Singularities of harmonic maps, Bull. Amer. Math. Soc. 34 (1997), 15-34. MR 1:397098
  • 9. J. Kigami and M.L. Lapidus, Weyl's problem for the spectral distribution of Laplacians on p.c.f. self-similar sets, Commun. Math. Phys. 158 (1993), 93-125. MR 94m:58225
  • 10. B.B. Mandelbrot, The Fractal Geometry of Nature, Freeman, San Francisco, 1982. MR 84h:00021
  • 11. P. Mattila, Lecture Notes on Geometric Measure Theory, Universidad de Extremadura, 1986. MR 89e:49037
  • 12. P. Mattila, M.S. Melnikov and J. Verdera, The Cauchy integral, analytic capacity, and uniform rectifiability, Ann. of Math. 144 (1996), 127-136. MR 1:405945
  • 13. F. Morgan, Geometric Measure Theory, A Beginner's Guide, Academic Press, 1988. MR 89f:49036
  • 14. D. Mumford (Reviewer), Variational methods in image segmentation by Jean-Michel Morel and Sergio Solimini, Bull. Amer. Math. Soc. 33 (1996), 211-216.
  • 15. D. Preiss, Geometry of measures in $\mathbb {R}^n$: distribution, rectifiability, and densities, Ann. of Math. 125 (1987), 537-643. MR 88d:28008
  • 16. C.A. Rogers, Hausdorff measures, Cambridge University Press, 1970. MR 43:7576
  • 17. L. Simon, Lectures on Geometric Measure Theory, Proceedings of the Centre for Mathematical Analysis, Australian National University, 3, 1983. MR 87a:49001
  • 18. S.J. Taylor, The measure theory of random fractals, Math. Proc. Cambridge Phil. Soc. 100 (1986), 383-406. MR 87k:60189

Review Information:

Reviewer: Christoph Bandt
Affiliation: Arndt-Universität Greifswald
Email: bandt@uni-greifswald.de
Journal: Bull. Amer. Math. Soc. 34 (1997), 323-327
MSC (1991): Primary 28-02; Secondary 28A75, 26B15, 30C85, 42B20, 49Q15
DOI: https://doi.org/10.1090/S0273-0979-97-00725-8
Review copyright: © Copyright 1997 American Mathematical Society
American Mathematical Society