A functional form of the isoperimetric inequality for the Gaussian measure

被引：27

作者：

Bobkov, S ^{[1
]}

机构：

[1] UNIV N CAROLINA,CTR STOCHAST PROC,DEPT STAT,CHAPEL HILL,NC 27599

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 1996年 / 135卷 / 01期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1006/jfan.1996.0002

中图分类号：

O1 [数学];

学科分类号：

0701 [数学]; 070101 [基础数学];

摘要：

Let g be a smooth function on R(n) with values in [0, 1]. Using the isoperimetric property of the Gaussian measure, it is proved that phi(Phi(-1)(Eg)) - E phi(Phi(-1)(g)) less than or equal to E\del g\. Conversely, this inequality implies the isoperimetric property of the Gaussian measure. (C) 1996 Academic Press, Inc.

引用

页码：39 / 49

页数：11

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