Affine images of compact convex sets and maximal measures

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F09%3A00207365" target="_blank" >RIV/00216208:11320/09:00207365 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Affine images of compact convex sets and maximal measures

Original language description

Let $phi:Xto Y$ be an affine continuous mapping of a compact convex set X onto a compact convex set Y. We show that the induced mapping $phi#$ need not map maximal measures on X to maximal measures on Y even in case $phi$ maps extreme points of X toextreme points of Y. This disproves Théoréme 6 of [S. Teleman, Sur les mesures maximales, C. R. Acad. Sci. Paris Sér. I Math. 318 (6) (1994) 525-528]. We prove the statement of Théoréme 6 under an additional assumption that extY is Lindelöf or Y is a simplex. We also show that under either of these two conditions injectivity of $phi$ on extX implies injectivity of $phi#$ on maximal measures. A couple of examples illustrate the results.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2009

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Bulletin des Sciences Mathematiques

ISSN

0007-4497

e-ISSN

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Volume of the periodical

133

Issue of the periodical within the volume

5

Country of publishing house

FR - FRANCE

Number of pages

8

Pages from-to

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UT code for WoS article

000268955000006

EID of the result in the Scopus database

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