Introduction to Geometric Probability

by

Daniel A. Klain and Gian-Carlo Rota



Table of Contents



Preface iv

Using this book vi

1 The Buffon needle problem 1
2 Valuation and integral 5
3 A discrete lattice 11
4 The intrinsic volumes for parallelotopes 27
5 The lattice of polyconvex sets 38
6 Invariant measures on Grassmannians 54
7 The intrinsic volumes for polyconvex sets 78
8 A characterization theorem for volume 88
9 Hadwiger's characterization theorem 107
10 Kinematic formulas for polyconvex sets 132
11 Polyconvex sets in the sphere 140
References 153

Index of symbols 160

Index 162


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