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Factorization Calculus and Geometric Probability - Encyclopedia of Mathematics and its Applications (Hardback)
  • Factorization Calculus and Geometric Probability - Encyclopedia of Mathematics and its Applications (Hardback)

Factorization Calculus and Geometric Probability - Encyclopedia of Mathematics and its Applications (Hardback)

Hardback 300 Pages / Published: 28/09/1990
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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.

Publisher: Cambridge University Press
ISBN: 9780521345354
Number of pages: 300
Weight: 585 g
Dimensions: 234 x 156 x 21 mm

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 Society
"The book is written in the characteristic style of the author, full of new and interesting ideas and, although in appearance the prerequisites are only standard courses on analysis and probability, it is not easy to read. It must be carefully thought out in many of its details, but the effort is well compensated by the great deal of information and new ways of thinking it supplies." L. A. Santalo, Mathematical Reviews
"The author of the present book, R.V. Ambartzumian, is one of the leading experts in the mentioned fields. He has influenced the development of integral and stochastic geometry by numerous, interesting results, new methods, and problems, a great part of which is presented in the monograph....highly recommended to mathematicians interested in integral and stochastic geometry. It is very stimulating because of the abundance of interesting results, models, and problems." J. Mecke, SIAM Review

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