On utilise le théorème de Hahn-Banach pour construire quelques fonctionnelles sur des espaces de fonctions continues. On caractérise la frontière de Choquet, et on donne des démonstrations simples :
a) du théorème de Bishop et de Leeuw avec des conditions de séparabilité ;
b) du théorème de Bauer.
@article{AIF_1963__13_1_111_0,
author = {Edwards, David Albert},
title = {On the representation of certain functionals by measures on the Choquet boundary},
journal = {Annales de l'Institut Fourier},
volume = {13},
year = {1963},
pages = {111-121},
doi = {10.5802/aif.133},
mrnumber = {26 \#5413},
zbl = {0112.34302},
language = {en},
url = {http://dml.mathdoc.fr/item/AIF_1963__13_1_111_0}
}
Edwards, David Albert. On the representation of certain functionals by measures on the Choquet boundary. Annales de l'Institut Fourier, Tome 13 (1963) pp. 111-121. doi : 10.5802/aif.133. http://gdmltest.u-ga.fr/item/AIF_1963__13_1_111_0/
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