Definition:Summation/Finite Support
< Definition:Summation(Redirected from Definition:Summation over Set with Finite Support)
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Definition
Let $G$ be an abelian group.
Let $S$ be a set.
Let $f: S \to G$ be a mapping.
Let the support $\map \supp f$ be finite.
Let $g$ be the restriction of $f$ to $\map \supp f$.
The summation of $f$ over $S$, denoted $\ds \sum_{s \mathop \in S} \map f s$, is the summation over the finite set $\map \supp f$ of $g$:
- $\ds \sum_{s \mathop \in S} \map f s = \sum_{s \mathop \in \map \supp f} \map g s$