Introduction to Geometric Probability

Klappentext The basic ideas of the subject and the analogues with enumerative combinatorics are described and exploited. Zusammenfassung The basic ideas of geometrical probability and the theory of shape are here presented in their natural framework. In this way! the relationship between the subject and enumerative combinatorics is more transparent! and the analogies can be more productively understood. Geometers and combinatorialists will find this a most stimulating and fruitful story. Inhaltsverzeichnis Introduction; 1. The Buffon needle problem; 2. Valuation and integral; 3. A discrete lattice; 4. The intrinsic volumes for parallelotopes; 5. The lattice of polyconvex sets; 6. Invariant measures on Grassmannians; 7. The intrinsic volumes for polyconvex sets; 8. A characterization theorem for volume; 9. Hadwiger's characterization theorem; 10. Kinematic formulas for polyconvex sets; 11. Polyconvex sets in the sphere; References; Index of symbols; Index.

Zusammenfassung
The basic ideas of geometrical probability and the theory of shape are here presented in their natural framework. In this way, the relationship between the subject and enumerative combinatorics is more transparent, and the analogies can be more productively understood. Geometers and combinatorialists will find this a most stimulating and fruitful story.

Inhalt
Introduction; 1. The Buffon needle problem; 2. Valuation and integral; 3. A discrete lattice; 4. The intrinsic volumes for parallelotopes; 5. The lattice of polyconvex sets; 6. Invariant measures on Grassmannians; 7. The intrinsic volumes for polyconvex sets; 8. A characterization theorem for volume; 9. Hadwiger's characterization theorem; 10. Kinematic formulas for polyconvex sets; 11. Polyconvex sets in the sphere; References; Index of symbols; Index.

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