Theory of Random Sets

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Springer Science & Business Media, Mar 30, 2006 - Mathematics - 488 pages

Stochastic geometry is a relatively new branch of mathematics. Although its predecessors such as geometric probability date back to the 18th century, the formal concept of a random set was developed in the beginning of the 1970s. Theory of Random Sets presents a state of the art treatment of the modern theory, but it does not neglect to recall and build on the foundations laid by Matheron and others, 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.

 

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Contents

Contents
1
Expectations of Random Sets
145
Expectations on lattices and in metric spaces
183
Minkowski Addition
195
Unions of Random Sets
241
Notes to Chapter 4
299
Notes to Chapter 5
378
Appendices
387
B Space of closed sets
398
Multifunctions and semicontinuity
409
F Convex sets
421
H Regular variation
428
References 435
453
List of Notation
463
Subject Index 475
474
Copyright

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About the author (2006)

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