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  3. Factorization Calculus and Geometric Probability
  • Cited by 53
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    • Publisher:
      Cambridge University Press
      Publication date:
      November 2011
      September 1990
      ISBN:
      9781139086561
      9780521345354
      9780521089784
      DOI:
      https://doi.org/10.1017/CBO9781139086561
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      0.585kg, 300 Pages
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      0.42kg, 300 Pages
      • Subjects:
      Mathematics (general), Mathematics, Abstract Analysis
      Series:
      Encyclopedia of Mathematics and its Applications (33)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Abstract Analysis
    Series:
    Encyclopedia of Mathematics and its Applications (33)
    Information

    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. 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.

    Reviews

    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.’

    Source: Bulletin of the London Mathematical Society

    Review of the hardback:‘An opera of real analysis…’

    Source: Bulletin of the American Mathematical Society

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