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

Abstract

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.