This paper has two major contributions: 1) Shafer’s belief functions are extended from finite sets to general universes (sets). 2) Belief function theory on a universe with countable focal elements is interpreted as a probability theory on the product space $\Omega$ x [0; 1] A counter intuitive point of a belief function is its ignoring the impact of the intersections among focal elements. One obvious intuitive rational is: The basic probability assignment (bpa) is a measurement of some disjoint ”information” on focal elements. Item #2 show that this disjoint ”information” is a partition (equivalence relation) on the product space. Here are interesting corollary and new exploration: 3) Belief function is an inner probability, if all focal elements are disjoint. 4) Issues for Bel of uncountable focal elements are lightly touched.