How do I create "double-struck" square brackets in math mode?

\documentclass[a4paper,12pt]{article}

\usepackage{stmaryrd}

\begin{document}

\begin{equation}
  f_Z\llbracket  x: y z t   \rrbracket      
\end{equation}

\end{document}

Use \llbracket and \rrbracket from fourier package (for example) for those doubled bracket symbols.

\documentclass{article}


\usepackage{mathtools}    
\usepackage{fourier}

\begin{document}
 $ f_{Z} \llbracket x \coloneqq y + z\rrbracket (\sigma) = [ x \mapsto Z ] (\sigma)$

\end{document}

If using the whole fourier package is too much, importing symbols might be an option: Import one symbol from `fourier`

Here's the version with import of the symbols (code copied from fourier.sty)

\documentclass{article}

\usepackage{mathtools}
\DeclareFontEncoding{FML}{}{}%
\DeclareFontSubstitution{FML}{futm}{m}{it}%
\DeclareFontEncoding{FMS}{}{}
\DeclareFontSubstitution{FMS}{futm}{m}{n}
\DeclareFontEncoding{FMX}{}{}
\DeclareFontSubstitution{FMX}{futm}{m}{n}
\DeclareSymbolFont{symbols}{FMS}{futm}{m}{n}%
\DeclareSymbolFont{largesymbols}{FMX}{futm}{m}{n}%

\DeclareMathDelimiter{\llbracket}{\mathopen}{symbols}{153}{largesymbols}{133}
\DeclareMathDelimiter{\rrbracket}{\mathclose}{symbols}{154}{largesymbols}{134}


\begin{document}
$ f_{Z} \llbracket x \coloneqq y + z\rrbracket (\sigma) = [ x \mapsto Z ] (\sigma)$

\end{document}

Please note the difference between the regular symbols f, x etc. from the screen shots.

In addition to the fourier and stmaryd packages, the mathabx package also provides "double-struck" square brackets; the macro names are \ldbrack and \rdbrack, respectively.

\documentclass{article}
\usepackage{mathabx} % for `\ldbrack` and `\rdbrack` macros
\begin{document}
$ f_{Z} \ldbrack x := y + z\rdbrack (\sigma) = [x\mapsto Z]\sigma$     
\end{document}