\(
\newcommand{\Ds}{\displaystyle}
\newcommand{\PP}{{\mathbb P}}
\newcommand{\RR}{{\mathbb R}}
\newcommand{\KK}{{\mathbb K}}
\newcommand{\CC}{{\mathbb C}}
\newcommand{\ZZ}{{\mathbb Z}}
\newcommand{\NN}{{\mathbb N}}
\newcommand{\TT}{{\mathbb T}}
\newcommand{\QQ}{{\mathbb Q}}
\newcommand{\Abs}[1]{{\left|{#1}\right|}}
\newcommand{\Floor}[1]{{\left\lfloor{#1}\right\rfloor}}
\newcommand{\Ceil}[1]{{\left\lceil{#1}\right\rceil}}
\newcommand{\sgn}{{\rm sgn\,}}
\newcommand{\Set}[1]{{\left\{{#1}\right\}}}
\newcommand{\Norm}[1]{{\left\|{#1}\right\|}}
\newcommand{\Prob}[1]{{{{\mathbb P}}\left[{#1}\right]}}
\newcommand{\Mean}[1]{{{{\mathbb E}}\left[{#1}\right]}}
\newcommand{\cis}{{\rm cis}\,}
\newcommand{\one}{{\mathbf 1}}
\newcommand{\One}[1]{{\bf 1}\left(#1\right)}
\renewcommand{\Re}{{\rm Re\,}}
\renewcommand{\Im}{{\rm Im\,}}
\renewcommand{\arg}{{\rm arg\,}}
\renewcommand{\Arg}{{\rm Arg\,}}
\renewcommand{\deg}{{\rm deg\,}}
\renewcommand{\vol}{{\rm vol\,}}
\newcommand{\ft}[1]{\widehat{#1}}
\newcommand{\FT}[1]{\left(#1\right)^\wedge}
\newcommand{\Lone}[1]{{\left\|{#1}\right\|_{1}}}
\newcommand{\Linf}[1]{{\left\|{#1}\right\|_\infty}}
\newcommand{\inner}[2]{{\langle #1, #2 \rangle}}
\)
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