Definition:Weight Function

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A weight function on a set $S$ is a mapping from $S$ to the real numbers:

$w: S \to \R$

It is common for the requirements of a specific application under discussion for the codomain of $w$ to be restricted to the positive reals:

$w: S \to \R_{\ge 0}$

The thing that determines whether a given mapping is a weight function depends more on how it is used.

Also see