https://hal-paris1.archives-ouvertes.fr/hal-02531787Bachir, MohammedMohammedBachirSAMM - SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) - UP1 - Université Paris 1 Panthéon-SorbonneDaniilidis, ArisArisDaniilidisUAB - Departament de Matemàtiques [Barcelona] - UAB - Universitat Autònoma de BarcelonaDIM-CMM, UMI CNRS 2807Extending the Choquet theory: Trace convexityHAL CCSD2020Choquet convexityExposed pointKrein-Milman theoremTrace-convexityBauer Maximum PrincipleVariational PrincipleExtreme point.[MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA]Bachir, Mohammed2020-04-03 20:03:342022-07-23 03:53:152020-04-06 09:52:27enPreprints, Working Papers, ...application/pdf1We introduce the notion of trace convexity for functions and respectively, for subsets of a compact topological space. This notion generalizes both classical convexity of vector spaces, as well as Choquet convexity for compact metric spaces. We provide new notions of trace-convexification for sets and functions as well as a general version of Krein-Milman theorem. We show that the class of upper semicontinuous convex-trace functions attaining their maximum at exactly one Choquet-boundary point is residual and we obtain several enhanced versions of the maximum principle which generalize both the classical Bauer's theorem as well as its abstract version in the Choquet theory. We illustrate our notions and results with concrete examples of three different types.