Introduction to Geometric Probability (Softcover) [3201]

Condition

VERY GOOD: This book is in very good condition, showing some wear and a small crease on the front cover.

Product Details

Continued from the back cover: "The theory of intrinsic volumes due to Hadwiger, McMullen, Santaló and others is presented, together with a complete and elementary proof of Hadwiger's characterization theorem of invariant measures in Euclideann -space. The theory of the Euler characteristic is developed from an integral-geometric point of view. The authors then provide the fundamental theorem of integral geometry, namely the kinematic formula. Finally, the analogies between invariant measures on polyconvex sets and measures on order ideals of finite partially ordered sets are investigated. The relationship between convex geometry and enumurative combinatorics motivates much of the presentation. Every chapter concludes with a list of unsolved problems. Geometers and combinatorialists will find this a stimulating and fruitful tale."

Chapters

1. The Buffon needle problem
2. Valuation and integral
3. A discrete lattice
4. The intrinsic volumes for parallelotopes
5. The lattice of polyconvex sets
6. Invariant measures on Grassmannians
7. The intrinsic volumes for polyconvex sets
8. A characterization theorem for volume
9. Hadwiger's characterization theorem
10. Kinematic formulas for polyconvex sets
11. Polyconvex sets in the sphere

The book concludes with Bibliography, Index of Symbols, and Index.