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Integral Geometry and Geometric Probability

Integral Geometry and Geometric Probability

2nd Edition


Part of Cambridge Mathematical Library

  • Date Published: October 2004
  • availability: Available
  • format: Paperback
  • isbn: 9780521523448

£ 69.99

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About the Authors
  • 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.

    • The standard reference for the area now available in the Cambridge Mathematical Library
    • Ideal as a reference for researchers or for graduate students wishing to enter the area
    • Subject finds applications in many other areas
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    Product details

    • Edition: 2nd Edition
    • Date Published: October 2004
    • format: Paperback
    • isbn: 9780521523448
    • length: 428 pages
    • dimensions: 219 x 156 x 21 mm
    • weight: 0.59kg
    • contains: 55 b/w illus.
    • availability: Available
  • Table of Contents

    Part I. Integral Geometry in the Plane:
    1. Convex sets in the plane
    2. Sets of points and Poisson processes in the plane
    3. Sets of lines in the plane
    4. Pairs of points and pairs of lines
    5. Sets of strips in the plane
    6. The group of motions in the plane: kinematic density
    7. Fundamental formulas of Poincaré and Blaschke
    8. Lattices of figures
    Part II. General Integral Geometry:
    9. Differential forms and Lie groups
    10. Density and measure in homogenous spaces
    11. The affine groups
    12. The group of motions in En
    Part III. Integral Geometry in En:
    13. Convex sets in En
    14. Linear subspaces, convex sets and compact manifolds
    15. The kinematic density in En
    16. Geometric and statistical applications: stereology
    Part IV. Integral Geometry in Spaces of Constant Curvature:
    17. Noneuclidean integral geometry
    18. Crofton's formulas and the kinematic fundamental formula in noneuclidean spaces
    19. Integral geometry and foliated spaces: trends in integral geometry.

  • Author

    Luis A. Santaló, Universidad de Buenos Aires, Argentina


    Mark Kac, Rockefeller University, New York

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