
Factorization Calculus and Geometric Probability
R. V. Ambartzumian(Author)
Cambridge University Press
Published on 28. September 1990
Book
Hardback
300 pages
978-0-521-34535-4 (ISBN)
Description
This unique book develops the classical subjects of geometric probability and integral geometry, and the more modern one of stochastic geometry, in rather a novel way to provide a unifying framework in which they can be studied. The author focuses on factorisation properties of measures and probabilities implied by the assumption of their invariance with respect to a group, in order to investigate non-trivial 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 non-specialist audience. Even in the later chapters, where the factorisation principles are applied to geometrical processes, the prerequisites are only standard courses on probability and analysis. The main ideas presented here have application to such areas as stereology and tomography, geometrical statistics, pattern and texture analysis. This book will be well suited as a starting point for individuals working in those areas to learn about the mathematical framework. It will also prove valuable as an introduction to geometric probability theory and integral geometry based on modern ideas.
Reviews / Votes
Review of the hardback: '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 Review of the hardback: 'An opera of real analysis...' Bulletin of the American Mathematical SocietyMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Dimensions
Height: 240 mm
Width: 161 mm
Thickness: 21 mm
Weight
617 gr
ISBN-13
978-0-521-34535-4 (9780521345354)
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Schweitzer Classification
Other editions
Additional editions

R. V. Ambartzumian
Factorization Calculus and Geometric Probability
E-Book
07/2013
1st Edition
Cambridge University Press
€47.49
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R. V. Ambartzumian
Factorization Calculus and Geometric Probability
Book
11/2008
Cambridge University Press
€68.10
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Previous edition
R. V. Ambartzumian
Factorization Calculus
Book
01/1990
Cambridge University Press
Unfortunately, price unknown
Article exhausted; check for reprint
Content
Preface; 1. Cavalieri principle and other prerequisites; 2. Measures invariant with respect to translations; 3. Measures invariant with respect to Euclidean motions; 4. Haar measures on groups of affine transformations; 5. Combinatorial integral geometry; 6. Basic integrals; 7. Stochastic point processes; 8. Palm distributions of point processes; 9. Poisson-generated geometrical processes; 10. Section through planar geometrical processes; References; Index.