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  • 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. (en)
Title
  • Affine images of compact convex sets and maximal measures
  • Affine images of compact convex sets and maximal measures (en)
skos:prefLabel
  • Affine images of compact convex sets and maximal measures
  • Affine images of compact convex sets and maximal measures (en)
skos:notation
  • RIV/00216208:11320/09:00207365!RIV10-GA0-11320___
http://linked.open...avai/riv/aktivita
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  • P(GA201/06/0018), P(GA201/07/0388), Z(MSM0021620839)
http://linked.open...iv/cisloPeriodika
  • 5
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  • 302105
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  • RIV/00216208:11320/09:00207365
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  • Affine; images; compact; convex; maximal; measures (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • FR - Francouzská republika
http://linked.open...ontrolniKodProRIV
  • [9D0391449CC2]
http://linked.open...i/riv/nazevZdroje
  • Bulletin des Sciences Mathematiques
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http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 133
http://linked.open...iv/tvurceVysledku
  • Kačena, Miroslav
  • Spurný, Jiří
http://linked.open...ain/vavai/riv/wos
  • 000268955000006
http://linked.open...n/vavai/riv/zamer
issn
  • 0007-4497
number of pages
http://localhost/t...ganizacniJednotka
  • 11320
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