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,
$49.95$
Michael Barnsley, Fractals everywhere, Academic Press, Inc., Boston, MA, 1988. MR 977274
Lennart Carleson, Selected problems on exceptional sets, Van Nostrand Mathematical Studies, No. 13, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0225986
Gerald A. Edgar, Measure, topology, and fractal geometry, Undergraduate Texts in Mathematics, Springer-Verlag, New York, 1990. MR 1065392, DOI 10.1007/978-1-4757-4134-6
K. J. Falconer, The geometry of fractal sets, Cambridge Tracts in Mathematics, vol. 85, Cambridge University Press, Cambridge, 1986. MR 867284
Kenneth Falconer, Fractal geometry, John Wiley & Sons, Ltd., Chichester, 1990. Mathematical foundations and applications. MR 1102677
Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York, Inc., New York, 1969. MR 0257325
Herbert Federer, Colloquium lectures on geometric measure theory, Bull. Amer. Math. Soc. 84 (1978), no. 3, 291–338. MR 467473, DOI 10.1090/S0002-9904-1978-14462-0
T. Venkatarayudu, The $7$-$15$ problem, Proc. Indian Acad. Sci., Sect. A. 9 (1939), 531. MR 0000001, DOI 10.1090/gsm/058
Jun Kigami and Michel L. Lapidus, Weyl’s problem for the spectral distribution of Laplacians on p.c.f. self-similar fractals, Comm. Math. Phys. 158 (1993), no. 1, 93–125. MR 1243717
Benoit B. Mandelbrot, The fractal geometry of nature, Schriftenreihe für den Referenten. [Series for the Referee], W. H. Freeman and Co., San Francisco, Calif., 1982. MR 665254
Pertti Mattila, Lecture notes on geometric measure theory, Publicaciones del Departamento de Matemáticas, Universidad de Extremadura [Publications of the Mathematics Department of the University of Extremadura], vol. 14, Universidad de Extremadura, Facultad de Ciencias, Departamento de Matemáticas, Badajoz, 1986. MR 931079
T. Venkatarayudu, The $7$-$15$ problem, Proc. Indian Acad. Sci., Sect. A. 9 (1939), 531. MR 0000001, DOI 10.1090/gsm/058
Frank Morgan, Geometric measure theory, Academic Press, Inc., Boston, MA, 1988. A beginner’s guide. MR 933756
14. D. Mumford (Reviewer), Variational methods in image segmentation by Jean-Michel Morel and Sergio Solimini, Bull. Amer. Math. Soc. 33 (1996), 211-216.
David Preiss, Geometry of measures in $\textbf {R}^n$: distribution, rectifiability, and densities, Ann. of Math. (2) 125 (1987), no. 3, 537–643. MR 890162, DOI 10.2307/1971410
C. A. Rogers, Hausdorff measures, Cambridge University Press, London-New York, 1970. MR 0281862
Leon Simon, Lectures on geometric measure theory, Proceedings of the Centre for Mathematical Analysis, Australian National University, vol. 3, Australian National University, Centre for Mathematical Analysis, Canberra, 1983. MR 756417
S. James Taylor, The measure theory of random fractals, Math. Proc. Cambridge Philos. Soc. 100 (1986), no. 3, 383–406. MR 857718, DOI 10.1017/S0305004100066160
- 1.
- M. Barnsley, Fractals Everywhere, Academic Press, 1988. MR 0977274
- 2.
- L. Carleson, Selected Problems on Exceptional Sets, van Nostrand, 1967. MR 0225986
- 3.
- G.A. Edgar, Measure, Topology, and Fractal Geometry, Springer, 1990. MR 1065392
- 4.
- K.J. Falconer, The Geometry of Fractal Sets, Cambridge University Press, 1985. MR 0867284
- 5.
- K.J. Falconer, Fractal Geometry: Mathematical Foundations and Applications, Wiley, 1990. MR 1102677
- 6.
- H. Federer, Geometric Measure Theory, Springer, 1969, reprinted 1996. MR 0257325
- 7.
- H. Federer, Colloquium lectures in geometric measure theory, Bull. Amer. Math. Soc. 84 (1978), 291-338. MR 0467473
- 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 1243717
- 10.
- B.B. Mandelbrot, The Fractal Geometry of Nature, Freeman, San Francisco, 1982. MR 0665254
- 11.
- P. Mattila, Lecture Notes on Geometric Measure Theory, Universidad de Extremadura, 1986. MR 0931079
- 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 0933756
- 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
: distribution, rectifiability, and densities, Ann. of Math. 125 (1987), 537-643. MR 0890162
- 16.
- C.A. Rogers, Hausdorff measures, Cambridge University Press, 1970. MR 0281862
- 17.
- L. Simon, Lectures on Geometric Measure Theory, Proceedings of the Centre for Mathematical Analysis, Australian National University, 3, 1983. MR 0756417
- 18.
- S.J. Taylor, The measure theory of random fractals, Math. Proc. Cambridge Phil. Soc. 100 (1986), 383-406. MR 0857718
Review Information:
Reviewer:
Christoph Bandt
Affiliation:
Arndt-Universität Greifswald
Email:
bandt@uni-greifswald.de
Journal:
Bull. Amer. Math. Soc.
34 (1997), 323-327
DOI:
https://doi.org/10.1090/S0273-0979-97-00725-8
Review copyright:
© Copyright 1997
American Mathematical Society
