On images of Borel measures under Borel mappings

被引：1

作者：

Gatzouras, D ^{[1
]}

机构：

[1] Univ Crete, Dept Math, Iraklion 71409, Crete, Greece

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2002年 / 130卷 / 09期

关键词：

convergence of a sequence of images of a measure; tight measure; Prohorov's theorem; characterization of images of a tight measure; Baire class 2 mapping;

D O I：

10.1090/S0002-9939-02-06434-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let X and Y be metric spaces. We show that the tight images of a (fixed) tight Borel probability measure mu on X, under all Borel mappings f : X --> Y, form a closed set in the space of tight Borel probability measures on Y with the weak*-topology. In contrast, the set of images of mu under all continuous mappings from X to Y may not be closed. We also characterize completely the set of tight images of mu under Borel mappings. For example, if mu is non-atomic, then all tight Borel probability measures on Y can be obtained as images of mu, and as a matter of fact, one can always choose the corresponding Borel mapping to be of Baire class 2.

引用

页码：2687 / 2699

页数：13