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This monograph, now in a thoroughly revised second edition, offers the latest research on random sets. It has been extended to include substantial developments achieved since 2005, some of them motivated by applications of random sets to econometrics and finance. The present volume builds on the foundations laid by Matheron and others, including the vast advances in stochastic geometry, probability theory, set-valued analysis, and statistical inference. 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. It is completely self-contained, systematic and exhaustive, with the full proofs that are necessary to gain insight. Aimed at research level, Theory of Random Sets will be an invaluable reference for probabilists; mathematicians working in convex and integral geometry, set-valued analysis, capacity and potential theory; mathematical statisticians in spatial statistics and uncertainty quantification; specialists in mathematical economics, econometrics, decision theory, and mathematical finance; and electronic and electrical engineers interested in image analysis.

Mathematics. --- Game theory. --- Probabilities. --- Physics. --- Statistics. --- Electrical 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. --- Random sets. --- Geometric probabilities --- Set theory --- Distribution (Probability theory. --- Computer engineering. --- Economic theory --- Political economy --- Social sciences --- Economic man --- Computers --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Math --- Science --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Design and construction --- Mathematical physics. --- Statistics . --- Electric engineering --- Engineering --- Physical mathematics --- Physics --- Games, Theory of --- Theory of games --- Mathematical models --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk