Closing the spacing for \sum_{\substack{}}\cdots\sum_{\substack{}}

Question

Here is the code I have that produces the output below. I wanted to learn if there is a way to close the gap around '\cdots'. And similarly between '=' and '\sum' on left, 'sum' and '\mathbb{P}' on right.

\sum_{\substack{x_T\in
    \mb{S}_T\\\nu_T\in\mb{P}^N(\mb{S}_T)}} \cdots
\sum_{\substack{x_1\in
    \mb{S}_1\\\nu_1\in\mb{P}^N(\mb{S}_1)}}

Note: If the solution is complicated, no need to spend time as this document is not required to be esthetic. I only want to learn. Also, not sure about the tag.

Answer 1

You're getting that wide spacing because of the width of the expressions in your \substack expression. Arguably that's not really what you want.

The simplest route to what you want is to use \! to insert negative thin spaces to tighten things up (I found three \! on either side of the \cdots looked ok. It's possible to make a wrapper around \substack that will cause LaTeX to ignore its width for spacing purpose, but that brings things too close together so I would lean against that option because you'll almost certainly end up with the subscripts bumping up against each other. Here's what I did and its results:

\newcommand{\Substack}[1]{\hbox to 0pt{\hss $\substack{ #1}$\hss}}

\[
  = \sum_{\Substack{x_T\in \mb{S}_T\\\nu_T\in\mb{P}^N(\mb{S}_T)}} \cdots
    \sum_{\Substack{x_1\in \mb{S}_1\\\nu_1\in\mb{P}^N(\mb{S}_1)}}
\]