The rule of combination of belief functions on infinite sets of possibilities is developed in this paper. The author continues his developments on Dempster’s theory on lower probabilities in order to generalize already-obtained results in the framework of “theory of evidence” that are important for approximate reasoning using such a generalization of probability theory.

The paper is dedicated to researchers and scientists interested in approximate reasoning based on Dempster-Shafer theory. While the presentation is clear for readers having a background in this theory, beginners should study some important references recommended in the text.

Structured in seven sections, the presentation covers lower and upper integration (§2); product belief functions, which generalize the idea of a product probability measure preserving the continuity and condensability properties (§3); the notion of “evidentially independent subalgebras” (§4); Dempster’s rule of conditioning (§5); Dempster’s rule of combination (§6); and the notion of “cognitively independent subalgebras” with respect to a belief function (§7).

In my opinion, this well-written paper on an important subject, with complete proofs, good argumentation, and well-established connections and citations of the relevant scientific literature, should be highlighted by scientists from both the mathematics and computer science fields.