\newcommand{\R}{\mathbb{R}} % reelle
\newcommand{\Z}{\mathbb{Z}} % ganze
\newcommand{\N}{\mathbb{N}} % natuerliche

\newcommand{\G}{\mathcal{G}} % Grobes Gitter
\newcommand{\F}{\mathcal{F}} % Feines Gitter
\newcommand{\U}{\mathcal{U}} % Übergangsbereich

\newcommand{\rfneq}[2]{\boldsymbol{r(}f_{f,\star}^\text{neq}, #1, #2\boldsymbol{)}}

\newcommand\numberthis{\addtocounter{equation}{1}\tag{\theequation}}

\newcommand{\V}[2]{\ensuremath{\begin{pmatrix}#1\\#2\end{pmatrix}}}
\newenvironment{rcases}{\left.\begin{aligned}}{\end{aligned}\right\rbrace}