On a class of integral inequalities and their measure-theoretic consequences
On a class of integral inequalities and their measure-theoretic consequences
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关于一类积分不等式及其测度论后果
DOI：
10.1016/0022-247x(80)90136-5
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发表时间：
1980
影响因子：
1.3
通讯作者：
B. Uhrin
中科院分区：
文献类型：
--
作者：
S. Dancs;B. Uhrin
本文讨论了Bonnesen和Fenchel [1]及Hadwiger [2]等经典著作意义下的积分几何中函数与测度的不等式。这些不等式的调查已变得越来越重要，近年来，因为它们与随机规划问题的连接被发现（Prekopa [3，41，Bore 11 [. 5，61）。数理统计的应用列表可以在Rinott [9]中找到。Bore 11 [6]的论文详细讨论了这类不等式及其应用和历史。概率论中Brunn-Minkowski经典不等式的USC：早已为人所知（安德森[7]，或最近，Davidovich et al. [S]）.本文的目的是给出已知不等式的新的简单证明，并证明一些新的不等式.我们只处理连续的情况。Leindlcr [lo，1 l]和Uhrin [12]研究了这种类型的离散不等式（对于无穷级数）。Uhrin [13]发现了这种类型的多维离散不等式与数的几何之间的有趣联系。
This paper deals with inequalities for functions and measures which belong to integral geometry, in the sense of the classical books by Bonnesen and Fenchel [1] and Hadwiger [2]. The investigation of these inequalities has become increasingly important in recent years since their connection with stochastic programming problems was discovered (Prekopa [3, 41, Bore11 [. 5, 61). A list of applications to mathematical statistics can be found in Rinott [9]. The paper of Bore11 [6] contains a detailed discussion of inequalities of this type together with applications and their history. The USC: of the Brunn-Minkowski classical inequality in probability theory has long been known (Anderson [7], or recently, Davidovich et al.[S]).The object of this paper is to give new simple proofs of known inequalities and to prove some new ones. We deal only with the continuous case. Discrete inequalities of this type (for infinite series) were investigated by Leindlcr [lo, 1 l] and Uhrin [12]. An interesting connection between a multidimensional discrete inequality of this type and the geometry of numbers has been discovered by Uhrin [13].