Integral Geometry and Geometric Probability
2nd Edition
Published on 28. October 2004
Book
Paperback/Softback
428 pages
978-0-521-52344-8 (ISBN)
Description
Now available in the Cambridge Mathematical Library, the classic work from Luis Santalo. 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.
More details
Series
Edition
2nd Revised edition
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Edition type
Revised edition
Product notice
Paperback (trade)
Illustrations
55 Line drawings, unspecified
Dimensions
Height: 229 mm
Width: 152 mm
Thickness: 25 mm
Weight
691 gr
ISBN-13
978-0-521-52344-8 (9780521523448)
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Schweitzer Classification
Persons
Content
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 Poincare 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.