The Brunn-Minkowski inequality for random sets

DOI10.1016/0047-259X(90)90052-JzbMath0705.60013WikidataQ29304552 ScholiaQ29304552MaRDI QIDQ918020

Richard A. Vitale

Publication date: 1990

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

zbMATH Keywords

convex hullBrunn-Minkowski inequalityrandom set

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Geometric probability and stochastic geometry (60D05) Set-valued functions (26E25) Set-valued set functions and measures; integration of set-valued functions; measurable selections (28B20) Set-valued maps in general topology (54C60) Selections in general topology (54C65) Inequalities and extremum problems involving convexity in convex geometry (52A40) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items (5)

The Brunn-Minkowski inequality ⋮ Brunn-Minkowski and Zhang inequalities for convolution bodies ⋮ A strong law of large numbers on the harmonic \(p\)-combination ⋮ Wasserstein barycenters over Riemannian manifolds ⋮ The translative expectation of a random set

Cites Work

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• Extremal properties of some geometric processes
• Expected convex hulls, order statistics, and Banach space probabilities
• Verallgemeinerung eines in der Statistik benötigten Satzes der Maßtheorie
• Brunn-Minkowski inequality and its aftermath
• A strong law of large numbers for random compact sets
• Integrals of set-valued functions
• The Integral of a Symmetric Unimodal Function over a Symmetric Convex Set and Some Probability Inequalities
• An application of the central limit theorem for banach-space-valued random variables to the theory of random sets
• A Generalization of Anderson's Theorem on Unimodal Functions
• The integral of an invariant unimodal function over an invariant convex set—an inequality and applications

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