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Introduction to Geometric Probability : Lezioni Lincee - Daniel A. Klain

Introduction to Geometric Probability

By: Daniel A. Klain, Gian-Carlo Rota, Luigi A. Radicati Di Brozolo (Editor)

Paperback | 9 February 1998

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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, Santalo 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.
Industry Reviews
'Geometers and combinatorialists will find this a stimulating and fruitful tale.' Fachinformationszentrum Karlsruhe ' ... a brief and useful introduction ...' European Mathematical Society

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Hardcover

Published: 9th February 1998

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