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Sur la génération des fonctions boréliennes fortement affines sur un convexe compact métrisable. (On the generation of strongly affine Borel functions on a metrizable convex compact set). (French) Zbl 0604.46012
On définit un filtre coanalytique sur les entiers tel que pour tout convexe compact métrisable K, les fonctions boréliennes fortement affine sur K, i.e. vérifiant les égalités barycentriques, soient exactement les limites simples suivant ce filtre de suites de fonctions affines continues sur K.

46A55 Convex sets in topological linear spaces; Choquet theory
46A50 Compactness in topological linear spaces; angelic spaces, etc.
46G05 Derivatives of functions in infinite-dimensional spaces
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[1] G. CHOQUET, Theory of capacities, Annales Inst. Fourier, Grenoble, 5 (1953-1954), 131-295. · Zbl 0064.35101
[2] G. CHOQUET, Remarques à propos de la démonstration d’unicité de P.-A. Meyer, (appendice), Séminaire de Théorie du Potentiel 6e année, exposé n° 8, IHP Paris, 1961-1962. · Zbl 0115.32402
[3] C. DELLACHERIE et P.-A. MEYER, Probabilités et potentiel, Tome 3, (chapitre X - 3), Hermann, Paris, 1984.
[4] M. KATÉTOV, On descriptive classification of functions, general topology and its relations to modern analysis and algebra III, Proceedings of the Third Prague Topological Symposium, 1971, pp. 235-242. · Zbl 0309.54015
[5] M. TALAGRAND, A new type of Borel affine functions, à paraître dans Compositio Mathematica. · Zbl 0562.46005
[6] Y. N. MOSCHOVAKIS, Descriptive set theory, Studies in Logic and the Foundations of Mathematics, 100, North Holland, 1980. · Zbl 0433.03025
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