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

页码：286 / 293

页数：8

共 17 条

[1]

Anderson T.W., 1955, P AM MATH SOC, V6, P170, DOI [10.2307/2032333, DOI 10.2307/2032333]

[2] STRONG LAW OF LARGE NUMBERS FOR RANDOM COMPACT SETS [J].