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
相关论文
共 50 条
  • [1] The Brunn-Minkowski inequality and nonconvex sets
    Ruzsa, IZ
    GEOMETRIAE DEDICATA, 1997, 67 (03) : 337 - 348
  • [2] A refined Brunn-Minkowski inequality for convex sets
    Figalli, A.
    Maggi, F.
    Pratelli, A.
    ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2009, 26 (06): : 2511 - 2519
  • [3] The Brunn-Minkowski inequality
    Gardner, RJ
    BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 39 (03) : 355 - 405
  • [4] THE φ-BRUNN-MINKOWSKI INEQUALITY
    Lv, S. -J.
    ACTA MATHEMATICA HUNGARICA, 2018, 156 (01) : 226 - 239
  • [5] Brunn-Minkowski Inequality
    Alonso-Gutierrez, David
    Bastero, Jesus
    APPROACHING THE KANNAN-LOVASZ-SIMONOVITS AND VARIANCE CONJECTURES, 2015, 2131 : 137 - 146
  • [6] A nonabelian Brunn-Minkowski inequality
    Jing, Yifan
    Tran, Chieu-Minh
    Zhang, Ruixiang
    GEOMETRIC AND FUNCTIONAL ANALYSIS, 2023, 33 (04) : 1048 - 1100
  • [7] Refinements of the Brunn-Minkowski Inequality
    Hernandez Cifre, Maria A.
    Yepes Nicolas, Jesus
    JOURNAL OF CONVEX ANALYSIS, 2014, 21 (03) : 727 - 743
  • [8] Companions to the Brunn-Minkowski inequality
    Niezgoda, Marek
    POSITIVITY, 2025, 29 (01)
  • [9] Generalizations of the Brunn-Minkowski inequality
    Liu, Juntong
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2016, 508 : 206 - 213
  • [10] The Dual φ-Brunn-Minkowski Inequality
    Shi, Wei
    Li, Tian
    Wang, Weidong
    MEDITERRANEAN JOURNAL OF MATHEMATICS, 2021, 18 (05)
12345