ENGLISH

Introduction to geometric probability

By Gian-Carlo Rota , Daniel A. Klain

Book information

Publisher
CUP
Year
1997
ISBN
9780521596541, 0521596548
LCC
QA273.5 .K47 1997
Open Library ID
OL415421M
Language
english
Format
DJVU
Filesize
1 MB (1188595 bytes)
Series
Lezioni Lincee
Pages
191\191
Library
Kolxo3
DPI
600
Time added
2010-11-11 16:01:50

Description

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.

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