A Yosida-Hewitt decomposition for totally monotone set functions on locally compact sigma-compact topological spaces
We prove for totally monotone set functions defined on the set of Borel sets of a locally compact a-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. (C) 2007 Elsevier Inc. All rights reserved.
totally monotone set functions yosida-hewitt's decomposition choquet's integral representation theorem