Definition:Extended Weight Function
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Definition
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:
- $\forall A \in \mathscr F : \map {w^+} A = \ds \sum_{a \mathop \in A} \map w a$
Sources
- 1976: Dominic Welsh: Matroid Theory ... (next) Chapter $19. \ \S 1.$ The greedy algorithm