Nonspecificity for infinite random sets of indexable type

In this document the Hartley-like-based measure of nonspecificity for finite random sets is extended to infinite random sets of indexable type. In the course of the paper, concepts defined in the realm of Dempster–Shafer evidence theory, like joint and marginal random sets and random set inclusion are also generalized. It is shown that the proposed measure is the unique one that fulfills a set of characterizing properties, and in addition corresponds to the one defined in the field of evidence theory when particularized to finite random sets.