= Belief function
{title2=$\operatorname{Bel}$}
The <belief function> induced by a <basic probability assignment> $m$ on a finite <sample space> $\Theta$ is
$$
\operatorname{Bel}(A)=\sum_{B\subseteq A}m(B).
$$
It counts evidence committed entirely inside $A$. If a random subset $S$ has <probability distribution> $m$, then $\operatorname{Bel}(A)=\mathbb P(S\subseteq A)$. This gives a concrete interpretation of the otherwise unusual summation over subsets.
For $m(\{r\})=0.6$, $m(\{r,b\})=0.4$, the singleton beliefs are $0.6$ and zero, although $\operatorname{Bel}(\{r,b\})=1$. The remaining mass is unresolved evidence, so additivity across the two singletons fails. A <belief function> is paired with the <plausibility function> $\operatorname{Pl}(A)=1-\operatorname{Bel}(A^c)$, describing evidence compatible with $A$.<Belief Functions: Introduction by Glenn Shafer>[Sections 1–2, nonadditive belief and uncommitted evidence]{ref}
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