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I am using the tufte-book class and want to have the captions of the figure enviroment in a different color, especially the word 'figure 1.1'. How can you do that?

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    Since configuration and package choice hugely influence the answer to this question, we need to to provide a minimal example of the setup you are currently using. You will see this request on most questions posed by new users. – daleif Aug 23 '15 at 19:56
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You can change the color of the caption using the \setcaptionfont macro provided by Tufte-LaTeX:

\documentclass{tufte-handout}

\usepackage{graphicx}
\usepackage{lipsum}% provides dummy text

% Change the color of the captions (but not sidenotes, margin notes, etc.)
\setcaptionfont{%
  \normalfont\footnotesize
  \color{red}% <-- set color here
}

\begin{document}

\lipsum[1]

\begin{figure}
  \includegraphics[width=\linewidth]{example-image}
  \caption{This is an example figure.}
\end{figure}

\lipsum[2]

\end{document}

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