. "8"^^ . . "5" . . "[9D0391449CC2]" . "Spurn\u00FD, Ji\u0159\u00ED" . . . . "0007-4497" . "Affine images of compact convex sets and maximal measures" . "Affine; images; compact; convex; maximal; measures"@en . "Bulletin des Sciences Mathematiques" . . "Affine images of compact convex sets and maximal measures"@en . . "11320" . "Ka\u010Dena, Miroslav" . . "302105" . "P(GA201/06/0018), P(GA201/07/0388), Z(MSM0021620839)" . . . . "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 Th\u00E9or\u00E9me 6 of [S. Teleman, Sur les mesures maximales, C. R. Acad. Sci. Paris S\u00E9r. I Math. 318 (6) (1994) 525-528]. We prove the statement of Th\u00E9or\u00E9me 6 under an additional assumption that extY is Lindel\u00F6f 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." . . "2"^^ . . . . "2"^^ . "FR - Francouzsk\u00E1 republika" . . . . . "RIV/00216208:11320/09:00207365!RIV10-GA0-11320___" . "000268955000006" . "Affine images of compact convex sets and maximal measures"@en . "Affine images of compact convex sets and maximal measures" . "133" . "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 Th\u00E9or\u00E9me 6 of [S. Teleman, Sur les mesures maximales, C. R. Acad. Sci. Paris S\u00E9r. I Math. 318 (6) (1994) 525-528]. We prove the statement of Th\u00E9or\u00E9me 6 under an additional assumption that extY is Lindel\u00F6f 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 . . . "RIV/00216208:11320/09:00207365" .