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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 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. An extensive, searchable bibliography to accompany the book is freely available via the web. The book will be an invaluable reference for probabilists, mathematicians in convex and integral geometry, set-valued analysis, capacity and potential theory, mathematical statisticians in spatial statistics and image analysis, specialists in mathematical economics, and electronic and electrical engineers interested in image analysis.

Random sets. --- Set theory. --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical --- Mathematics --- Geometric probabilities --- Set theory --- Distribution (Probability theory. --- Mathematics. --- Statistics. --- Computer engineering. --- Economic theory. --- Probability Theory and Stochastic Processes. --- Game Theory, Economics, Social and Behav. Sciences. --- Theoretical, Mathematical and Computational Physics. --- Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. --- Electrical Engineering. --- Economic Theory/Quantitative Economics/Mathematical Methods. --- Economic theory --- Political economy --- Social sciences --- Economic man --- Computers --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Math --- Science --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Design and construction --- Probabilities. --- Game theory. --- Mathematical physics. --- Statistics . --- Electrical engineering. --- Electric engineering --- Engineering --- Physical mathematics --- Physics --- Games, Theory of --- Theory of games --- Mathematical models --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk