Surface Measures Generated by Differentiable Measures

被引：7

作者：

Bogachev, Vladimir I. ^{[1
]}

Malofeev, Ilya I. ^{[2
]}

机构：

[1] Natl Res Univ, Higher Sch Econ, Moscow, Russia

[2] Moscow MV Lomonosov State Univ, Dept Mech & Math, Moscow 119991, Russia

来源：

POTENTIAL ANALYSIS | 2016年 / 44卷 / 04期

基金：

俄罗斯科学基金会;

关键词：

Malliavin calculus; Surface measure; Differential measure; Gaussian measure; METRIC MEASURE-SPACES; BV FUNCTIONS; SOBOLEV FUNCTIONS; INFINITE; FINITE; CAPACITIES; PERIMETER; INTEGRALS; CALCULUS; GEOMETRY;

D O I：

10.1007/s11118-015-9530-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study surface measures on level sets of functions on general probability spaces with measures differentiable along vector fields and suggest a new simple construction. Our construction applies also to level sets of mappings with values in finite-dimensional spaces. The standard surface measures arising for Gaussian measures in the Malliavin calculus can be obtained in this way. A positive answer is given to a question raised by M. Rockner concerning continuity of surface measures with respect to a parameter.

引用

页码：767 / 792

页数：26

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