Integral geometry and geometric probability

著者

• Santaló, Luis A. (Luis Antonio)

書誌事項

Integral geometry and geometric probability

Luis A. Santaló ; with a foreword by Mark Kac

（Cambridge mathematical library）

Cambridge University Press, 2004

2nd ed

注記

First edition published: Addison-Wesley, 1976 -- T.p. verso

Reprinted with revisions, 1979 -- T.p. verso

Bibliography: p. 363-394

Includes Indexes

内容説明・目次

内容説明

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.

目次

• 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.

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BA69314586
• ISBN:
  • 0521523443
• 出版国コード: uk
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Cambridge
• ページ数/冊数: xvii, 404 p.
• 大きさ: 23 cm
• 分類:
  • DC21 : 516.362
• 件名:
  • LCSH : Integral geometry
  • LCSH : Geometric probabilities
• 親書誌ID:
  • BA0151012X