A Yosida-Hewitt decomposition for totally monotone games on locally compact sigma-compact topological spaces

URL des Cahiers : https://halshs.archives-ouvertes.fr/CAHIERS-MSECahiers de la Maison des Sciences Economiques 2005.87 - ISSN : 1624-0340We prove for totally monotone games defined on the set of Borel sets of a locally compact s-compact topological space a similar decomposition theorem to the famous Yosida-Hewitt's one for finitely additive measures. This way any totally monotone decomposes into a continuous part and a pathological part which vanishes on the compact subsets. We obtain as corollaries some decompositions for finitely additive set functions and for minitive set functions.Nous obtenons une décomposition à la Yosida-Hewitt pour les jeux totalement monotones définis sur un espace topologique localement compact et s-compact. Ainsi tout jeu totalement monotone se décompose en une partie continue et une partie pathologique s'annulant sur les compacts. Nous obtenons en corollaires des décompositions pour les fonctions d'ensemble additives et pour les fonctions d'ensemble minitives

A Yosida-Hewitt decomposition for totally monotone games on locally compact sigma-compact topological spaces.

We prove for totally monotone games defined on the set of Borel sets of a locally compact sigma-compact topological space a similar decomposition theorem to the famous Yosida-Hewitt's one for finitely additive measures. This way any totally monotone decomposes into a continuous part and a pathological part which vanishes on the compact subsets. We obtain as corollaries some decompositions for finitely additive set functions and for minitive set functions.Choquet's integral representation theorem, Yosida-Hewitt decomposition, totally monotone games.