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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...

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.

This monograph examines limit theorems and the laws of large numbers for scaled unions of independent, identically-distributed random sets. The results generalize well-known facts about the theory of extreme values. Limiting distributions are characterized and found for random closed sets.

This is the first full-length study of how the theory of random sets can be applied in econometrics.