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.