\begin{definition}[Definition:Extended Weight Function]
Let $S$ be a set.
Let $\mathscr F$ be the set of all finite subsets of $S$.
Let $w: S \to \R$ be a weight function.
The '''extended weight function''' of $w$ is the function $w^+: \mathscr F \to \R$ defined by:
:$\forall A \in \mathscr F : \map {w^+} A = \ds \sum_{a \mathop \in A} \map w a$
\end{definition}