Abstract:Subadditivity of capacities is defined initially on the compact sets and need not extend to all sets. This paper explores to what extent subadditivity holds. It presents some incidental results that are valid for all subadditive capacities. The main result states that for all hull-additive capacities (a class that contains the strongly subadditive capacities) there is countable subadditivity on a class at least as large as the universally measurable sets (so larger than the analytic sets).
Keywords: capacities, subadditive capacities, sup measures, hull-additive capacities, vague and narrow topologies, lattice of capacities
AMS Subject Classification: Primary 28A12; Secondary 28C15