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Factorization Calculus and Geometric Probability : Encyclopedia of Mathematics and Its Applications - R. V. Ambartzumian

Factorization Calculus and Geometric Probability

Encyclopedia of Mathematics and Its Applications

Hardcover Published: 28th September 1990
ISBN: 9780521345354
Number Of Pages: 300

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The classical subjects of geometric probability and integral geometry, and the more modern one of stochastic geometry, are developed here in a novel way to provide a framework in which they can be studied. The author focuses on factorization properties of measures and probabilities implied by the assumption of their invariance with respect to a group, in order to investigate nontrivial factors. The study of these properties is the central theme of the book. Basic facts about integral geometry and random point process theory are developed in a simple geometric way, so that the whole approach is suitable for a nonspecialist audience. Even in the later chapters, where the factorization principles are applied to geometrical processes, the only prerequisites are standard courses on probability and analysis. The main ideas presented have application to such areas as stereology and geometrical statistics and this book will be a useful reference book for university students studying probability theory and stochastic geometry, and research mathematicians interested in this area.

From the hardback review: 'The authors presented themselves with an enormous task in gathering material from widely scattered areas to illustrate a single theme. It is a measure of how well they have succeeded that everything now seems coherent and interwoven. For this they deserve our sincere thanks.' Bulletin of the London Mathematical Society From the hardback review: 'An opera of real analysis...' Bulletin of the American Mathematical Society

Preface
Cavalieri principle and other prerequisites
Measures invariant with respect to translations
Measures invariant with respect to Euclidean motions
Haar measures on groups of affine transformations
Combinatorial integral geometry
Basic integrals
Stochastic point processes
Palm distributions of point processes
Poisson-generated geometrical processes
Section through planar geometrical processes
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521345354
ISBN-10: 0521345359
Series: Encyclopedia of Mathematics and Its Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 300
Published: 28th September 1990
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 23.4 x 15.6  x 1.7
Weight (kg): 0.6