THE BRUNN-MINKOWSKI INEQUALITY FOR RANDOM SETS

被引：12
|
作者：
VITALE, RA
机构：
来源：
JOURNAL OF MULTIVARIATE ANALYSIS | 1990年 / 33卷 / 02期
基金：
美国国家科学基金会;
关键词：
Anderson's inequality; Brunn-Minkowski inequality; multivariate density; random set; selection; set-valued expectation; unimodality;
D O I：
10.1016/0047-259X(90)90052-J
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
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. © 1990.
引用
收藏
页码：286 / 293
页数：8
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