10

I need to use a notation for the restriction of a measure to a set. It is similar to \mu \llcorner A, but I want the symbol defined by \llcorner to be bigger. I can't seem to find the right command for this.

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The result I want is something like the symbol in the pictures. The second picture is from Evans and Gariepy. The third one is from Federer's Geometric Measure Theory, so I don't think they are just isolated notations.

5
  • 1
    Could you post a picture of where you have seen that notation? In this document, for instance, the notation for the restriction of a measure \mu to a set A seems to be \left.\mu\right\rvert_A.
    – jub0bs
    Apr 6, 2013 at 23:29
  • 2
    @Jubobs You probably mean \mu\big|_{A}
    – egreg
    Apr 6, 2013 at 23:34
  • @egreg You must be right. The vertical bar is not a delimiter here...
    – jub0bs
    Apr 6, 2013 at 23:35
  • 2
    @Jubobs Not only that: \left. adds an unwanted space (and \right too).
    – egreg
    Apr 6, 2013 at 23:36
  • I have seen the Jubobs notation and the same but with a vertical harpoon instead of the vertical bar. But never seen that notation.
    – Manuel
    Apr 7, 2013 at 10:54

3 Answers 3

7

This shape is simple enough to build with rules:

Sample output

\documentclass{article}

\newcommand{\mres}{\mathbin{\vrule height 1.6ex depth 0pt width
0.13ex\vrule height 0.13ex depth 0pt width 1.3ex}}

\begin{document}

\( \mu \mres B(A) \)

\end{document}

There is also \niv in the nath fonts.

7

You can build the Evans and Gariepy notation with

\documentclass{article}

\usepackage{graphicx}

\newcommand{\measurerestr}{%
  \,\raisebox{-.127ex}{\reflectbox{\rotatebox[origin=br]{-90}{$\lnot$}}}\,%
}

\begin{document}
$\mu\measurerestr A,$
\end{document}

enter image description here

With picture mode we can choose between the three styles. I provided \mresA, \mresB and \mresC, but you should choose one and stick with it. Adjust the parameters at leisure.

\documentclass{article}
\usepackage{amsmath}
\usepackage{pict2e}

% syntactic sugar
\newcommand{\xmathpalette}[2]{%
  \mathchoice
    {#1\displaystyle\textfont{#2}}
    {#1\textstyle\textfont{#2}}
    {#1\scriptstyle\scriptfont{#2}}
    {#1\scriptscriptstyle\scriptscriptfont{#2}}
}

\makeatletter

\newcommand{\mres@thickness}[1]{\dimexpr1.5\fontdimen8 #13\relax}

\newcommand{\mresA}{\mspace{3mu}{\xmathpalette\mresA@\relax}\mspace{3mu}}
\newcommand{\mresA@}[3]{%
  \begingroup
  \setlength\unitlength{%
    \dimexpr\fontcharht#21`A-0.5\mres@thickness{#2}% height of capital letters
  }%
  \raisebox{0.5\dimexpr\mres@thickness{#2}}{%
    \begin{picture}(1,1)
      \roundcap\roundjoin
      \linethickness{\mres@thickness{#2}}% default rule thickness in the extension font
      \polyline(0,1)(0,0)(1,0)
    \end{picture}%
   }%
  \endgroup
}

\newcommand{\mresB}{\mspace{5mu}{\xmathpalette\mresB@\relax}\mspace{5mu}}
\newcommand{\mresB@}[3]{%
  \begingroup
  \setlength\unitlength{%
    \dimexpr0.8\fontcharht#21`A-0.5\mres@thickness{#2}% 80% height of capital letters
  }%
  \raisebox{0.5\dimexpr\mres@thickness{#2}}{%
    \begin{picture}(0.5,1)
      \roundcap\roundjoin
      \linethickness{\mres@thickness{#2}}% default rule thickness in the extension font
      \polyline(0,1)(0,0)(0.5,0)
    \end{picture}%
   }%
  \endgroup
}

\newcommand{\mresC}{\mspace{3mu}{\xmathpalette\mresC@\relax}\mspace{3mu}}
\newcommand{\mresC@}[3]{%
  \begingroup
  \setlength\unitlength{%
    \dimexpr0.8\fontcharht#21`A-0.5\mres@thickness{#2}% 80% height of capital letters
  }%
  \raisebox{0.5\dimexpr\mres@thickness{#2}}{%
    \begin{picture}(1,1)
      \roundcap\roundjoin
      \linethickness{\mres@thickness{#2}}% default rule thickness in the extension font
      \polyline(0,1)(0,0)(1,0)
    \end{picture}%
   }%
  \endgroup
}
\makeatother

\begin{document}

$\mu \mresA B(A)=\mu(B\cap A)$

$\scriptstyle \mu \mresA B(A)=\mu(B\cap A)$

$\mu \mresB B(A)=\mu(B\cap A)$

$\scriptstyle \mu \mresB B(A)=\mu(B\cap A)$

$\mu \mresC B(A)=\mu(B\cap A)$

$\scriptstyle \mu \mresC B(A)=\mu(B\cap A)$

\end{document}

enter image description here

2
  • That's great. Thank you. So there isn't any predefined symbol for this... Apr 7, 2013 at 12:36
  • @BeniBogosel Never seen before. And texdoc symbols didn't reveal anything useful.
    – egreg
    Apr 7, 2013 at 13:02
1

The resmes package provides the Federer's notation for the restriction of a measure:

\usepackage{resmes}

...

$\mu\resmes E$.

Restriction of measure 1

It works also in subscripts and superscripts:

$E_{\mu\resmes A}^{\eta\resmes B}$

Restriction of measure 2

The package is still under development but it's usable now. If you want to report a bug or to add a new feature you can visit the official page of the resmes package.

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