The Brunn-Minkowski inequality for random sets

The Brunn-Minkowski inequality asserts a concavity feature of the volume functional under convex addition of sets. Among its applications has been Anderson's treatment of multivariate densities. Here we present a generalization which interprets the inequality in terms of random sets. This provides a natural proof of Mudholkar's generalized Anderson-type inequality.

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Year of publication:	1990
Authors:	Vitale, Richard A.
Published in:	Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 33.1990, 2, p. 286-293
Publisher:	Elsevier
Keywords:	Anderson's inequality Brunn-Minkowski inequality multivariate density random set selection set-valued expectation unimodality

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005006434