Invariant and quasi-invariant measures on infinite-dimensional spaces

被引：4

作者：

Kozlov, V. V. ^{[1
]}

Smolyanov, O. G. ^{[2
]}

机构：

[1] Russian Acad Sci, Steklov Inst Math, Moscow 119991, Russia

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

来源：

DOKLADY MATHEMATICS | 2015年 / 92卷 / 03期

基金：

俄罗斯基础研究基金会;

关键词：

Hilbert Space; DOKLADY Mathematic; Gaussian Measure; Canonical Embedding; Infinite Dimensional Space;

D O I：

10.1134/S1064562415060290

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Extensions of locally convex topological spaces are considered such that finite cylindrical measures which are not countably additive on their initial domains turn out to be countably additive on the extensions. Extensions of certain transformations of the initial spaces with respect to which the initial measures are invariant or quasi-invariant to the extensions of these spaces are described. Similar questions are considered for differentiable measures. The constructions may find applications in statistical mechanics and quantum field theory.

引用

页码：743 / 746

页数：4

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