Riesz decompositions and subtractivity for excessive measures

The convex cone of excessive measures of a right Markov process is an example of a superharmonic semigroup in the abstract potential theory developed by Arsove and Leutwiler. We show that their theory of Riesz decompositions can be sharpened in the case of excessive measures. In particular there is always a Riesz decomposition relative to a given potential cone (resp. harmonic cone). An element of an ordered convex cone is subtractive if each majorant is a specific majorant. This notion of subtractivity features prominently in the theory of harmonic cones. We give a complete characterization of the subtractive elements in the cone of excessive measures.The research of both authors was supported in part by NSF Grant DMS 87-21347.