| dc.contributor.author |
Gatzouras, D |
en |
| dc.date.accessioned |
2014-06-06T06:44:52Z |
|
| dc.date.available |
2014-06-06T06:44:52Z |
|
| dc.date.issued |
2002 |
en |
| dc.identifier.issn |
0002-9939 |
en |
| dc.identifier.uri |
http://62.217.125.90/xmlui/handle/123456789/2114 |
|
| dc.subject |
convergence of a sequence of images of a measure |
en |
| dc.subject |
tight measure |
en |
| dc.subject |
Prohorov's theorem |
en |
| dc.subject |
characterization of images of a tight measure |
en |
| dc.subject |
Baire class 2 mapping |
en |
| dc.subject.classification |
Mathematics, Applied |
en |
| dc.subject.classification |
Mathematics |
en |
| dc.title |
On images of Borel measures under Borel mappings |
en |
| heal.type |
journalArticle |
en |
| heal.language |
English |
en |
| heal.publicationDate |
2002 |
en |
| heal.abstract |
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. |
en |
| heal.publisher |
AMER MATHEMATICAL SOC |
en |
| heal.journalName |
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY |
en |
| dc.identifier.issue |
9 |
en |
| dc.identifier.volume |
130 |
en |
| dc.identifier.isi |
ISI:000175568300024 |
en |
| dc.identifier.spage |
2687 |
en |
| dc.identifier.epage |
2699 |
en |