TITLE: Mathematical notation for a conditional sum
QUESTION [11 upvotes]: I'm looking for the correct way to define a sum of all elements in a set that fullfill a certain condition.
Example:
$$
n(A) = \frac{\sum_{F \in A}{
\begin{cases}
A_F\text{ is }\mathrm{NULL} & w_F\\
\text{else} & 0
\end{cases}}}{\sum_{F \in A}{w_F}}
$$
A is to supposed to be a record with a number of fields $F$. $A_F$ is the value of field F in the record A. $w_F$ is a weight associated with the Field $F$. I want to calculate how much percent of the record is NULL weighted according to $w_F$.
What I want to know is if this below is a valid way to formulate this or if there is a better way.
If someone has some pointers on a more formal / mathematical notation for database/records I would also be very grateful.
Thanks!

REPLY [4 votes]: I know it is not any cool notation, but maybe you can simply define a dummy set, one that satisfies all your conditions, and then, make the sum of wf on each element of this dummy set .
By adding a dummy set B, this part of your formula
$$\sum_{F \in A}{
\begin{cases}
A_F\text{ is }\mathrm{NULL} & w_F\\
\text{else} & 0
\end{cases}}$$
could be transformed into
$$
\sum_{F \in B}{w_F}
$$
Then add at the end of your formula that set B is all the elements f of set A for which Af is null:
$$B=\{f \in A | A_f\text{ is }\mathrm{NULL}\}
$$
Thus, my final answer to your question would look like this:
$$
n(A) = \frac{\sum_{F \in B}{w_F}}{\sum_{F \in A}{w_F}}
$$
where
$$B=\{f \in A | A_f\text{ is }\mathrm{NULL}\}
$$
**Also, I don't know yet if this notation is allowed:
$$
n(A) = \frac{\sum_{F \in \{f \in A | A_f\text{ is }\mathrm{NULL}\}}{w_F}}{\sum_{F \in A}{w_F}}
$$ but it is the integration of the B set definition into one big formula. I personnaly think that defining B on a separated formula is clearer, but I guess sometimes we need to use only one formula.