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Now available in the Cambridge Mathematical Library, the classic work from Luis Santaló. Integral geometry originated with problems on geometrical probability and convex bodies. Its later developments, however, have proved to be useful in several fields ranging from pure mathematics (measure theory, continuous groups) to technical and applied disciplines (pattern recognition, stereology). The book is a systematic exposition of the theory and a compilation of the main results in the field. The volume can be used to complement courses on differential geometry, Lie groups or probability or differential geometry. It is ideal both as a reference and for those wishing to enter the field.
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Geometric probabilities. --- Geometry --- Problems, exercises, etc.
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Acqui 2006 --- Geometric probabilities --- Integral geometry
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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.
Stochastic geometry. --- Geometric probabilities. --- Factorization (Mathematics) --- Mathematics --- Probabilities --- Geometry --- Stochastic geometry --- Geometric probabilities
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Probability theory --- Geometric probabilities --- Integral geometry --- 519.2 --- Geometry, Integral --- Geometry, Differential --- Probabilities --- Probability. Mathematical statistics --- Geometric probabilities. --- Integral geometry. --- 519.2 Probability. Mathematical statistics --- Géometrie intégrale
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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.
Stochastic geometry --- Factorization (Mathematics) --- Geometric probabilities --- 519.21 --- Geometry --- Probabilities --- Mathematics --- Probability theory. Stochastic processes --- Geometric probabilities. --- Stochastic geometry. --- Factorization (Mathematics). --- 519.21 Probability theory. Stochastic processes
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