Commit a899309b authored by Michael Kohlhase's avatar Michael Kohlhase

tweaks

parent 59555b95
......@@ -18,5 +18,9 @@
the triangle inequality for $d$ follows from that for $\anormOp$.
\end{spfstep}
\end{sproof}
\end{mhmodnl}
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......@@ -2,14 +2,18 @@
\begin{definition}
Ist $\realmorethan{p}1$ eine \mtrefii[realnumbers?real-number]{reelle}{Zahl} und
$\inset{\ntupli{x}1n}{\ndim\RealNumbers{n}}$, so nennen wir
\[\fundefeq{x}{\pnorm{p}x}{\realpower[basebrack]{\Sumfromto{i}1n{\realabsval{x_i}}}{\frac1p}}\]
\[\fundefeq{p,x}{\pnorm{p}x}{\realpower[basebrack]{\Sumfromto{i}1n{\realabsval{x_i}}}{\frac1p}}\]
seine \defi[name=pnorm]{$p$-Norm} (auch \defi[name=pnorm]{$\ell_p$-Norm} oder \defi[name=pnorm]{$L^p$-Norm}).
\end{definition}
\begin{definition}
Wir nennen die \mtrefi[?pnorm]{1-Norm} auch \defi[name=taxicab-norm]{Summennorm}
oder \defi[name=taxicab-norm]{Betragssummennorm}, und die \mtrefi[?pnorm]{2-Norm} the
\defii{Euklidsche}{Norm} oder \defii[name=Euclidean-norm]{Euklidsche}{L"ange}.
oder \defi[name=taxicab-norm]{Betragssummennorm}
\end{definition}
\begin{definition}
Die \mtrefi[?pnorm]{2-Norm} hei"st auch \defii{Euklidsche}{Norm} oder
\defii[name=Euclidean-norm]{Euklidsche}{L"ange}.
\end{definition}
\end{mhmodnl}
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......@@ -2,13 +2,16 @@
\begin{definition}
Let $\realmorethan{p}1$ be a \trefii[realnumbers]{real}{number} and
$\inset{\ntupli{x}1n}{\ndim\RealNumbers{n}}$, then we call
\[\fundefeq{x}{\pnorm{p}x}{\realpower[basebrack]{\Sumfromto{i}1n{\realabsval{x_i}}}{\frac1p}}\]
\[\fundefeq{p,x}{\pnorm{p}x}{\realpower[basebrack]{\Sumfromto{i}1n{\realabsval{x_i}}}{\frac1p}}\]
its \defi[name=pnorm]{$p$-norm} (also \defi[name=pnorm]{$\ell_p$-norm} or \defi[name=pnorm]{$L^p$-norm}).
\end{definition}
\begin{definition}
The \mtrefi[?pnorm]{1-norm} is called the \defii{taxicab}{norm}, and the
\mtrefi[?pnorm]{2-norm} the \defii{Euclidean}{norm} or the
The \mtrefi[?pnorm]{1-norm} is often called the \defii{taxicab}{norm}.
\end{definition}
\begin{definition}
The \mtrefi[?pnorm]{2-norm} the \defii{Euclidean}{norm} or the
\defii[name=Euclidean-norm]{Euclidean}{length}.
\end{definition}
\end{mhmodnl}
......
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