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}

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}

\mu
to a set A seems to be\left.\mu\right\rvert_A
.\mu\big|_{A}
\left.
adds an unwanted space (and\right
too).