Weighted Sum

CATEGORIES ABOUT WEIGHT FUNCTION

DISCRETE WEIGHTS

In the discrete setting, a weight
function

w: A 	o {\Bbb R}^+

is a positive function defined on a Discrete Set ''A'', which is typically
Finite or Countable . The weight function

w(a) := 1

corresponds to the ''unweighted'' situation in which
all elements have equal weight. One can then apply this weight to various concepts.

If

:

f: A 	o {\Bbb R}

is a Real -valued Function , then the unweighted Sum of ''f'' on ''A'' is

:

\sum_{a \in A} f(a)

;

but for a ''weight function''

:

w: A 	o {\Bbb R}^+

,

the weighted sum is

:

\sum_{a \in A} f(a) w(a)

.

One common application of weighted sums arises in Numerical Integration .

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