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In the usual Latex document classes, is there a simple way to have a background colour behind the footnotes only? It would probably help the reader in the organization of a page between main text and footnotes.

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If you place footnotes at the bottom of the page, with footnote marks and smaller type, I doubt that colour background will help the reader. –  Sveinung May 17 '12 at 6:56
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I have not tried this yet, but I can imagine that the colorbox environment from the standard color package might work for this. Use this in your preamble:

\usepackage{color}

And create your footnote like this:

\footnote{\colorbox{declared-color}{text}}
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The problem with that is that the footnote will no longer get broken across pages. This really has to be done in the output routine when \box\footins is getting used. –  user9588 May 17 '12 at 8:40
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