Factorization Calculus and Geometric Probability

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Hardcover | 31 December 1990

At a Glance

Hardcover
300 Pages

Dimensions(cm)
16.6 x 24.1 x 2.3

Hardcover

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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.

Industry Reviews

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

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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.

Factorization Calculus and Geometric Probability

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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