Countably additive Möbius transforms for belief functions on Polish spaces

We use Choquet’s integral representation theorem (Choquet, 1954) [5] to derive σσ-additive Möbius transforms for totally monotone capacities vv defined on the Borel sets of a Polish space ΩΩ and having certain continuity properties. Several results in the literature follow as corollaries.

► We study extreme points of sets of belief functions with various continuity properties. ► We derive sigma-additive Möbius transforms for continuous belief functions. ► We establish simple representations for Choquet integrals w.r.t. ► belief functions. ► We obtain two earlier characterizations of outer (resp. ► sigma) continuous belief functions.