The default version of the \DoubleSpacing
command in memoir
sets regular text double spaced but footnotes and captions etc., as single spaced. However, there is a starred version of the command that will make everything double spaced.
\documentclass{memoir}
\usepackage{kantlipsum}
\DoubleSpacing*
\begin{document}
\kant[1] This is some text\footnote{\kant[2]} Some more text.
\end{document}
If for some reason you only want footnotes to be double spaced, but captions still single spaced, you can modify the formatting of the footnote text independently.
Page 236 of the memoir
manual shows the parameters that control the footnote formatting. The macro \foottextfont
can be redefined to make double spaced footnotes:
\documentclass{memoir}
\usepackage{kantlipsum}
\DoubleSpacing
\renewcommand\foottextfont{\footnotesize\DoubleSpacing}
\begin{document}
\kant[1] This is some text\footnote{\kant[2]} Some more text.
\end{document}
