Vertical dots in \substack

Question

I need to stack a large number of expressions below a sum sign. Using \substack and \vdots as in the code below
\sum_{\substack{a_1 \in A_1\\ \vdots \\ a_k \in A_k}}
gives a pretty awful result, as the vertical dots are much closer to the bottom line than to the top one.
Is there a way to center the dots between the two lines? I tried to use \mathstrut to increase a little bit the spacing between the dots and the bottom line, but the increase is too small and apparently it does not stack up when repeating the command.

Answer 1

You can fine-tune vertical spacing after \\ with \\[...] like:

\sum_{\substack{a_1  \in  A_1\\[-4pt] \vdots  \\[2pt]  a_k  \in A_k}}

Result:

Answer 2

You may want smaller and less spaced dots. Here's a way, which mimicks the definition of \vdots.

\documentclass{article}
\usepackage{amsmath}
\makeatletter
\newcommand{\svdots}{%
  \vbox{\fontsize{\sf@size}{\sf@size pt}\linespread{0.3}\selectfont
    \kern0.2\baselineskip
    \hbox{.}\hbox{.}\hbox{.}%
    \kern0.1\baselineskip
  }%
}
\makeatother
\begin{document}
[
\sum_{\substack{a_1  \in  A_1\ \svdots  \  a_k  \in A_k}}
]
\end{document}