Integral Geometry and Geometric Probability
Integral Geometry and Geometric Probability
2nd Edition
October 2004
Available
Paperback
9780521523448
£77.99
GBPPaperback
USD
eBook
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
Product details
October 2004Paperback
9780521523448
428 pages
219 × 156 × 21 mm
0.59kg
55 b/w illus.
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.
