Definition:Normalized Weight Function

Let $S = \left \langle {x_1, x_2, \ldots, x_n}\right \rangle$ be a sequence of real numbers.
Let $W \left({x}\right)$ be a weight function to be applied to the elements of $S$.
Then $W$ is defined as being normalized if:
$\displaystyle \sum_x W \left({x}\right) = 1$