Theory of Random Sets recalls and builds on the foundations laid by Matheron and others to present a state of the art treatment of the modern theory, including the vast advances in stochastic geometry, probability theory, set-valued analysis, and statistical inference of the 1990s. The book is entirely self-contained, systematic and exhaustive, with the full proofs that are necessary to gain insight. 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 are often varying in the current literature to establish it as a natural part of modern probability theory, and to provide a platform for future development.

The first systematic exposition of random sets theory since Matheron (1975), with full proofs, exhaustive bibliographies and literature notes Interdisciplinary connections and applications of random sets are emphasised throughout Fixes terminology and notation that are often very varying in the literature, so providing a platform for future development of the theory Accompanied by an extensive searchable bibliography, available via the web

Autorentext

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

Inhalt
Random Closed Sets and Capacity Functionals.- Expectations of Random Sets.- Minkowski Addition.- Unions of Random Sets.- Random Sets and Random Functions. Appendices: Topological Spaces.- Linear Spaces.- Space of Closed Sets.- Compact Sets and the Hausdorff Metric.- Multifunctions and Continuity.- Measures and Probabilities.- Capacities.- Convex Sets.- Semigroups and Harmonic Analysis.- Regular Variation. References.- List of Notation.- Name Index.- Subject Index.