Basic probability assignment ($m$)

On a finite sample space $\Theta$, a basic probability assignment in Dempster-Shafer theory is a function on its power set satisfyingThe mass $m(B)$ is support committed to $B$ as a whole, without allocating it among the elements of $B$. Thus $m$ is a probability distribution over subsets, and generally is not an additive probability measure on $\Theta$.

For $\Theta =\{r,b\}$, let $m(\{r\})=0.6$ and $m(\Theta )=0.4$. The second mass expresses unresolved support between $r$ and $b$; it is not a claim that $b$ has probability $0.4$. This assignment induces belief function value $0.6$ and plausibility function value one for $\{r\}$. Ordinary additive probability is recovered when all nonzero masses are on singleton subsets.^[ref]