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The representations of linear functionals by measures on sets of extreme points

Errett Bishop; Karel De Leeuw — 1959

Annales de l'institut Fourier

Soit $X$ un compact, $B$ un espace vectoriel de fonctions numériques continues sur $X$ (muni de la norme classique), séparant les points de $X$ et contenant les constantes. On note $M (B)$ l’ensemble des $x$ de $X$ tels que toute mesure positive $μ$ sur $X$ pour laquelle on ait pour tout $f \in B$ : $f (x) = \int f d μ$ soit nécessairement la mesure de masse 1 portée par $x$ . On veut représenter les éléments de $B^{*}$ par des mesures portées par $M (B)$ ; un théorème de Choquet en montre la possibilité lorsque...

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