Geodesic
Continuous selector of representative measures and the space of faces of a~convex compactum
Matematičeskie zametki, Tome 22 (1977) no. 6, pp. 897-906

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A sufficient condition for the existence of a continuous selector of representative measure, concentrated at the extreme points of a convex metrizable compactum, is considered. A necessary condition for the existence of such a selector is deduced. An example is given of a convex compactum with a closed set of extreme points, for which no continuous selector exists. 
@article{MZM_1977_22_6_a10,
     author = {N. N. Makarov},
     title = {Continuous selector of representative measures and the space of faces of a~convex compactum},
     journal = {Matemati\v{c}eskie zametki},
     pages = {897--906},
     publisher = {mathdoc},
     volume = {22},
     number = {6},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_22_6_a10/}
}
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N. N. Makarov. Continuous selector of representative measures and the space of faces of a~convex compactum. Matematičeskie zametki, Tome 22 (1977) no. 6, pp. 897-906. http://geodesic.mathdoc.fr/item/MZM_1977_22_6_a10/