s is defined as $s : {1,2,3}$
To describe the function that filters values great that $a$ where $a = 2$ and multiplies result by 4, is this correct :
$$ \sum_{s \in S} : [ s > a] \cdot 4$$
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$\Sigma$ denotes a summation, which is not what you want I think. If I understand your question correctly then you want $${s\in S\mid s>a}$$ – user2520938 May 13 '17 at 09:24
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@user2520938 whats the | symbol ? why not use 'such that' instead ? – blue-sky May 13 '17 at 09:26
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3$\mid$ essentially means "such that". You don't use "such that" because its longer, and less readable. The notation I used above is completely standard. See https://en.wikipedia.org/wiki/Set-builder_notation – user2520938 May 13 '17 at 09:27
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@user2520938 that article also mentions using colon as alternative which is notation I'm more familiar with, thanks. – blue-sky May 13 '17 at 09:29
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That notation is called an Iverson bracket (no hyperlink b/c phone). It evaluates a proposition inside to 1 if true and 0 if false. It can be used to filter items inside a sum, but it is more common to define a new set based on $S$ and sum over that. – Greg Nisbet Feb 20 '19 at 22:16