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%%  Ein Beispiel der DANTE-Edition
%%  Mathematiksatz mit LaTeX
%%  3. Auflage
%%  Beispiel 10-02-1 auf Seite 214.
%%  Copyright (C) 2018 Herbert Voss
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%%  It may be distributed and/or modified under the conditions
%%  of the LaTeX Project Public License, either version 1.3
%%  of this license or (at your option) any later version.
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\begin{document}
\begin{equation}\addtolength{\arraycolsep}{-3pt}
I(z)=\delta_{0}\left\{\begin{array}{lcrcl}
 D+z & \quad & -D & \le z\le & -p\\
 D-\frac{1}{2}\left(p-\frac{z^{2}}{p}\right) &\quad& -p & \le z\le &\phantom{-}p\\
 D-z & \quad & p & \le z\le & \phantom{-}D
\end{array}\right.
\end{equation}
\end{document}