On the fiber bundle structure of the space of belief functions

The study of finite non-additive measures or “belief functions” has been recently posed in connection with combinatorics and convex geometry. As a matter of fact, as belief functions are completely specified by the associated belief values on the events of the frame on which they are defined, they can be represented as points of a Cartesian space. The space of all belief functions B or “belief space” is a simplex whose vertices are b.f. focused on single events. In this paper we present an alternative description of the space of belief functions in terms of differential geometric notions. The belief space possesses indeed a recursive fiber bundle structure inherently related to the mass assignment mechanism, in which basic probability is recursively assigned to events of increasing size. A formal proof of the decomposition of B into bases and fibers and their characterization as simplices are provided.