Introduction to Geometric Probability (Hardcover) (ISBN-13: 9780521593625)

Here is the first modern introduction to geometric probability, also known as integral geometry, presented at an elementary level, requiring little more than first-year graduate mathematics. Klein and Rota present the theory of intrinsic volumes due to Hadwiger, McMullen, Santal and others, along with a complete and elementary proof of Hadwiger's characterization theorem of invariant measures in Euclidean n-space. They develop the theory of the Euler characteristic from an integral-geometric point of view. The authors then prove 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 enumerative combinatorics motivates much of the presentation. Every chapter concludes with a list of unsolved problems.

Author: Daniel A. Klain, Gian-Carlo Rota
ISBN-10: 052159362X
ISBN-13: 9780521593625
Publisher: Cambridge University Press
Language: English
Published: 12/11/1997
Pages: 196
Format: Hardcover
Weight: 0.88lbs
Size: 8.50h x 5.50w x 0.56d