Does the colon appearing at the bottom of the summation notation reads as "such that?"

Is there an alternate way of writing the notation in more familiar forms?
Thank you.
Does the colon appearing at the bottom of the summation notation reads as "such that?"

Is there an alternate way of writing the notation in more familiar forms?
Thank you.
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With $S$ in $T$ and $e$ in $S$ or with $S$ as an element of $T$ and $e$ as an element of $S$ or something along those lines depending on what kind of objects $S$ $T$ and $e$ are.