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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F09%3A00207365%21RIV10-GA0-11320___
rdf:type
n16:Vysledek skos:Concept
dcterms:description
Let $\phi:X\to Y$ 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 to extreme 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. Let $\phi:X\to Y$ 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 to extreme 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.
dcterms:title
Affine images of compact convex sets and maximal measures Affine images of compact convex sets and maximal measures
skos:prefLabel
Affine images of compact convex sets and maximal measures Affine images of compact convex sets and maximal measures
skos:notation
RIV/00216208:11320/09:00207365!RIV10-GA0-11320___
n3:aktivita
n18:P n18:Z
n3:aktivity
P(GA201/06/0018), P(GA201/07/0388), Z(MSM0021620839)
n3:cisloPeriodika
5
n3:dodaniDat
n11:2010
n3:domaciTvurceVysledku
n9:8684308 n9:3116085
n3:druhVysledku
n14:J
n3:duvernostUdaju
n19:S
n3:entitaPredkladatele
n12:predkladatel
n3:idSjednocenehoVysledku
302105
n3:idVysledku
RIV/00216208:11320/09:00207365
n3:jazykVysledku
n15:eng
n3:klicovaSlova
Affine; images; compact; convex; maximal; measures
n3:klicoveSlovo
n4:maximal n4:compact n4:convex n4:measures n4:Affine n4:images
n3:kodStatuVydavatele
FR - Francouzská republika
n3:kontrolniKodProRIV
[9D0391449CC2]
n3:nazevZdroje
Bulletin des Sciences Mathematiques
n3:obor
n8:BA
n3:pocetDomacichTvurcuVysledku
2
n3:pocetTvurcuVysledku
2
n3:projekt
n6:GA201%2F07%2F0388 n6:GA201%2F06%2F0018
n3:rokUplatneniVysledku
n11:2009
n3:svazekPeriodika
133
n3:tvurceVysledku
Spurný, Jiří Kačena, Miroslav
n3:wos
000268955000006
n3:zamer
n7:MSM0021620839
s:issn
0007-4497
s:numberOfPages
8
n13:organizacniJednotka
11320