Expose la théorie de la représentation intégrale dans les cônes convexe, due à Gustave Choquet, et plusieurs de ses applications à l'analyse : théorèmes classiques de Bochner-Weil et de Bernstein, théorème de Choquet-Deny, axomatiques Brelot et Bauer en théorie du pentiel, résultats de Talagrand sur les mesures et capacités invariantes, et de Royer et Yor sur les mesures quasi invariantes. ©Electre 2024
This monograh is mainly devoted to the theory of integral representation in convex cones due to G. Choquet and to several of its applications to Analysis :
Classical theorems of Bochner-Weil and of Berstein, theorem of Choquet-Deny, axiomatics of Brelot an Bauer in potential theory, results of Talagrand concerning invariant measures and capacities and those of Royer and Yor concerning Quasi-invariant measures in field theory.
This book is accessible to a student with a Master's degrees M1 and M2, with emphasis on analysis, and can be considered as an introduction to the richness and variety of the subjects.
The three tools created by G. Choquet in this framework (weakly complete cones, caps, conical measures) are also studied for themselves. Moreover, there are also useful in other fields close to Analysis : zonoforms and vector measures, statistical decision spaces. bireticulated cones and normal cones contained in Banach spaces. Remark that in the postface G. Choquet relates the thought process which led him to find out the three tools mentioned above.
Paru le : 21/11/2006
Thématique : Mathématiques Appliquées
Auteur(s) : Auteur : Richard Becker
Éditeur(s) :
Hermann
Collection(s) : Travaux en cours
Série(s) : Non précisé.
ISBN : Non précisé.
EAN13 : 9782705666712
Reliure : Broché
Pages : XIII-251
Hauteur: 24.0 cm / Largeur 17.0 cm
Épaisseur: 1.5 cm
Poids: 460 g
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