## Introduction to Geometric Probability

by

Daniel A. Klain and
Gian-Carlo Rota

This is a modern introduction to geometric probability, also
known as integral geometry. The subject is presented at an elementary
level, requiring little more than first year graduate mathematics. The
theory of intrinsic volumes due to Hadwiger, McMullen, Santaló, and
others is presented, along with a complete and elementary proof of
Hadwiger's characterization theorem for invariant valuations in Euclidean
*n*-space. The theory of the Euler characteristic is developed 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 valuations on polyconvex sets and
valuations 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. Geometers and
combinatorialists will find this a stimulating and fruitful tale.

The book can be ordered through
Amazon.com or your favorite local bookstore. You can also contact the
publisher, Cambridge University
Press.

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