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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, setvalued 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 selfcontained, 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, setvalued 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.
⚠️ WARNING (California Proposition 65):
This product may contain chemicals known to the State of California to cause cancer,
birth defects, or other reproductive harm.
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