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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