Book Review
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MathSciNet review:
1566802
Full text of review:
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Book Information:
Author:
G. Matheron
Title:
Random sets and integral geometry
Additional book information:
Wiley, New York, 1975, xxiii+261 pp., $18.95.
1. W. Blaschke, Vorlesungen über integral Geometrie, Teubner, Leipzig, 1936-7.
2. G. Buffon, Essai d'arithmétique morale, Supplément à l'Histoire Naturelle, vol. 4, 1777.
Gustave Choquet, Theory of capacities, Ann. Inst. Fourier (Grenoble) 5 (1953/54), 131–295 (1955). MR 80760
4. M. W. Crofton, "Probability", in Encyclopaedia Britannica, 9th ed., 1885.
D. G. Kendall, Foundations of a theory of random sets, Stochastic geometry (a tribute to the memory of Rollo Davidson), Wiley, London, 1974, pp. 322–376. MR 0423465
M. G. Kendall and P. A. P. Moran, Geometrical probability, Griffin’s Statistical Monographs & Courses, No. 10, Hafner Publishing Co., New York, 1963. MR 0174068
J. F. C. Kingman, Random secants of a convex body, J. Appl. Probability 6 (1969), 660–672. MR 254891, DOI 10.1017/s0021900200026693
Victor Klee, Research Problems: What is the Expected Volume of a Simplex Whose Vertices are Chosen at Random from a Given Convex Body?, Amer. Math. Monthly 76 (1969), no. 3, 286–288. MR 1535340, DOI 10.2307/2316377
R. E. Miles, Poisson flats in Euclidean spaces. I. A finite number of random uniform flats, Advances in Appl. Probability 1 (1969), 211–237. MR 259977, DOI 10.2307/1426218
L. A. Santaló, Introduction to integral geometry, Publ. Inst. Math. Univ. Nancago, II, Hermann & Cie, Paris, 1953. MR 0060840
- 1.
- W. Blaschke, Vorlesungen über integral Geometrie, Teubner, Leipzig, 1936-7.
- 2.
- G. Buffon, Essai d'arithmétique morale, Supplément à l'Histoire Naturelle, vol. 4, 1777.
- 3.
- G. Choquet, Theory of capacities, Ann. Inst. Fourier (Grenoble) 5 (1953/54), 131-295 (1955). MR 18, 295. MR 0080760
- 4.
- M. W. Crofton, "Probability", in Encyclopaedia Britannica, 9th ed., 1885.
- 5.
- D. G. Kendall, Foundations of a theory of random sets, Stochastic Geometry, Wiley, New York and London, 1974. MR 423465
- 6.
- M. G. Kendall and P. A. P. Moran, Geometrical probability, Griffin's Statistical Monographs and Courses, no. 10, Hafner, New York, 1963. MR 30 #4275. MR 174068
- 7.
- J. F. C. Kingman, Random secants of a convex body, J. Appl. Probability 6 (1969), 660-672. MR 40 #8098. MR 254891
- 8.
- V. Klee, What is the expected volume of a simplex whose vertices are chosen at random from a given convex body? Amer. Math. Monthly 76 (1969), 236-238. MR 1535340
- 9.
- R. E. Miles, Poisson flats in Euclidean spaces. I. A finite number of random uniform flats, Advances in Appl. Probability 1 (1969), 211-237. MR 41 #4606. MR 259977
- 10.
- L. A. Santaló, Introduction to integral geometry, Actualités Sci. Indust., no. 1198, Hermann, Paris, 1953. MR 15, 736. MR 60840
Review Information:
Reviewer:
J. F. C. Kingman
Journal:
Bull. Amer. Math. Soc.
81 (1975), 844-847
DOI:
https://doi.org/10.1090/S0002-9904-1975-13853-5
