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Microstructure. --- Stochastic 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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This work is about random measures stationary with respect to a possibly non-transitive group action. It contains chapters on Palm Theory, the Mass-Transport Principle and Ergodic Theory for such random measures. The thesis ends with discussions of several new models in Stochastic Geometry (Cox Delauney mosaics, isometry stationary random partitions on Riemannian manifolds). These make crucial use of the previously developed techniques and objects.

mass-transport principle --- Random measure --- ergodic theory --- Stochastic Geometry --- Palm theory

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Stochastic geometry. --- Géométrie stochastique. --- Mathématiques --- Geometrie convexe --- Colloque --- Geometrie convexe --- Colloque

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Stochastic geometry. --- Géométrie stochastique. --- Mathématiques --- Geometrie integrale --- Geometrie convexe --- Corps convexes --- Geometrie integrale --- Geometrie convexe --- Corps convexes