# Skip specifying sets under summation signs

I have a couple of summations that all have the notation below them that s is an element of S, k is an element of K, etc. The set S or K is not given but assumed to be generally known.

$$\sum_{k \in K} X_k$$

and, for example

$$\sum_{s \in S} Y_s$$

Because I have so many of these summations and only three relevant sets, I think I have to note "s is an element of S", "k is an element of K", etc under every summation sign.

Would it also be possible to just state the following at the beginning of my series of summations, and skip the separate notation under each summation sign?

"For all summations, the following is valid":

$${s \in S} , {k \in K}$$

and then note the summations as follows:

$$\sum_{} X_k$$

$$\sum_{} Y_s$$

• While I might read that as you intend, it would not be correct to write it like this. – Tobias Kildetoft Nov 30 '13 at 18:59
• I think a better wording would be something like "In all the summations below, the summation variable $s$ is intended to range over $S$, and $k$ is intended to range over $K$." The point is to make it obvious that you're introducing a notational convention, not asserting that some statements are valid in the sense of being part of your line of reasoning. With this sort of preamble, I think your simplified notation is OK. – Andreas Blass Nov 30 '13 at 20:22