The Brunn-Minkowski inequality for random sets

Richard A. Vitale

Journal of Multivariate Analysis, 1990, vol. 33, issue 2, 286-293

Abstract: 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.

Keywords: Anderson's; inequality; Brunn-Minkowski; inequality; multivariate; density; random; set; selection; set-valued; expectation; unimodality (search for similar items in EconPapers)
Date: 1990
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