Factorization Calculus and Geometric Probability: 33 (Encyclopedia of Mathematics and its Applications, Series Number 33) - Softcover

Ambartzumian, R. V.

Softcover

ISBN 10: 0521089786 ISBN 13: 9780521089784

Publisher: Cambridge University Press, 2009

Synopsis

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.

About this title

Review

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

Book 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.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2009
• Language: English
• ISBN 10: 0521089786
• ISBN 13: 9780521089784
• Binding: Paperback
• Edition number: 1
• Number of pages: 300