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Ensembles fermés aléatoires, ensembles semi-markoviens et polyèdres poissoniens

Published online by Cambridge University Press:  01 July 2016

G. Matheron*
Affiliation:
Centre de Morphologie Mathématique, Fontainebleau

Abstract

Random set theory is closely connected with integral geometry. After a general description, based upon the Choquet theorem, the semi-Markovian property is defined and characterized in terms of integral geometry. Applications are made to Poisson polytopes characterized by conditional invariance properties.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 1972 

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References

Bibliographie

[1] Bourbaki, N. (1965) Eléments de Mathématiques, Fasc. XIII, Intégration. Hermann, Paris.Google Scholar
[2] Choquet, G. (1953–54) Theory of capacities. Ann. Inst. Fourier (Grenoble) V, 131295.Google Scholar
[3] Delfiner, P. (1971) A generalization of the concept of size. 3rd Int. Cong. for Stereology, Berne. (A paraître).Google Scholar
[4] Hadwiger, H. (1957) Vorlesungen über Inhalt, Oberfläche und Isoperimetrie. Springer, Berlin.Google Scholar
[5] Kendall, M. G. et Moran, P. A. P. (1963) Geometrical Probability. Hafner, New York.Google Scholar
[6] Matheron, G. (1967) Eléments pour une Théorie des Milieux Poreux. Masson, Paris.Google Scholar
[7] Matheron, G. (1969) Théorie des Ensembles Aléatoires. Cahiers du Centre de Morphologie Mathématique, Fontainebleau. Fasc. 4.Google Scholar
[8] Matheron, G. (1971) Random sets theory, and its applications to stereology. 3rd Int. Cong. for Stereology, Berne. (A paraître).Google Scholar
[9] Matheron, G. (1971) Les polyèdres poissoniens isotropes. 3ème Symposium Européen sur la Fragmentation, Cannes. (A paraître).Google Scholar
[10] Miles, R. E. (1964) Random polygons determined by random lines in a plane. Proc. Nat. Acad. Sci. USA, 52, 901907; II 1157–1160.CrossRefGoogle ScholarPubMed
[11] Miles, R. E. (1969) Poisson flats in euclidean space. Adv. Appl. Prob. 1, 211237.Google Scholar
[12] Miles, R. E. (1970) A synopsis of Poisson flats in euclidean spaces. Izv. Akad. Nauk Armjan. SSR 3, 263285.Google Scholar
[13] Miles, R. E. (1971) Poisson flats in euclidean space, Part II. Adv. Appl. Prob. 3, 143.CrossRefGoogle Scholar
[14] Neveu, J., (1964) Bases Mathématiques du Calcul des Probabilités. Masson, Paris.Google Scholar
[15] Serra, J. (1967) But et réalisation de l'analyseur de textures. Revue de l'Industrie Minérale 49, 933.Google Scholar
[16] Serra, J. (1969) Introduction à la Morphologie Mathématique. Cahiers du Centre de Morphologie Mathématique, Fontainebleau Fasc. 3.Google Scholar