Theory of Random Sets

Comprehensively covers the theory of random sets

Explores interdisciplinary connections and applications of the theory

Extensive and updated bibliography

Includes latest developments in the field

Comprehensively covers the theory of random sets Explores interdisciplinary connections and applications of the theory Extensive and updated bibliography Includes latest developments in the field

Autorentext
Ilya Molchanov is Professor of Probability Theory at the Department of Mathematical Statistics and Actuarial Science at the University of Bern, Switzerland.

Zusammenfassung
It shows the various interdisciplinary relationships of random set theory within other parts of mathematics, and at the same time fixes terminology and notation that often vary in the literature, establishing it as a natural part of modern probability theory and providing a platform for future development.

Inhalt
1 Random Closed Sets and Capacity Functionals.- 2 Expectations of Random Sets.- 3 Minkowski Sums.- 4 Unions of Random Sets.- 5 Random Sets and Random Functions.- A Topological spaces and metric spaces.- B Linear spaces.- C Space of closed sets.- D Compact sets and the Hausdorff metric.- E Multifunctions and semicontinuity.- F Measures and probabilities.- G Capacities.- H Convex sets.- I Semigroups, cones, and harmonic analysis.- J Regular variation.- References.