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commands.sty
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%!TEX root = ./ThesisRomainbrault.tex
\newcommand{\xdownarrow}[1]{%
{\left\downarrow\vbox to #1{}\right.\kern-\nulldelimiterspace}
}
\DeclareMathOperator*{\argmin}{arg\,min}
\DeclareMathOperator*{\argmax}{arg\,max}
\DeclareMathOperator{\Tr}{{\mathbf{Tr}}}
\DeclareMathOperator*{\sign}{sign}
\DeclareMathOperator{\lspan}{\overline{span}\;}
\DeclareMathOperator{\vect}{\bigoplus}
\DeclareMathOperator*{\Vect}{\bigoplus}
\DeclareMathOperator{\jacobian}{\mathbf{J}}
\DeclareMathOperator{\vectorize}{\mathbf{vec}}
\DeclareMathOperator*{\esssup}{ess\,sup}
\newcommand{\ima}{\text{im}\;}
\newcommand{\Ima}{\text{Im}\;}
\newcommand{\Ker}{\text{Ker}\;}
\newcommand{\Dom}{\text{Dom}\;}
\newcommand{\ec}{\mathrm{e}\mkern1mu}
\newcommand{\iu}{{\mathrm{i}\mkern1mu}}
\newcommand{\operator}[1]{\text{#1}}
% Florence's notations.
% \def\expectation{{\mathbb{E}}}
% \def\variance{{\mathbb{V}}}
% \def\probability{{\mathbb{P}}}
%\def\covari{{\math{Cov}}
% Romain's notations.
\newcommand{\expectation}{{\mathbf{{E}}}}
\newcommand{\variance}{{\mathbf{{Var}}}}
\newcommand{\covariances}{{\mathbf{Cov}}}
\newcommand{\probability}{{\mathbf{{Pr}}}}
\newcommand{\Leb}{\mathbf{Leb}}
\newcommand{\Haar}{\mathbf{Haar}}
\newcommand{\Radon}{\mathbf{Rad}}
\newcommand{\param}{\theta}
\newcommand{\minimiser}{\hat\theta}
\newcommand{\parameter}{\theta}
\newcommand{\idim}{d}
\newcommand{\odim}{p}
\newcommand{\myinv}[1]{#1^{-1}}
\newcommand{\FT}[1]{\mathcal{F}\left[#1\right]}
\newcommand{\IFT}[1]{\mathcal{F}^{-1}\left[#1\right]}
\newcommand{\MGF}{\text{MGF}}
\newcommand{\intdim}{\text{IntDim}}
\newcommand{\rank}{\text{Rank}}
% \newcommand{\dim}{\text{Dim}}
\newcommand{\seq}[1]{\boldsymbol{\mathbf{#1}}}
\newcommand{\derivative}[2]{\frac{\partial {#1}}{\partial {#2}}}
\newcommand{\lderivative}[2]{\frac{\partial}{\partial {#2}} {#1}}
\newcommand{\derivativeat}[3]{\left. \frac{\partial {#1}}{\partial {#2}}
\right|_{\scriptscriptstyle {#2}={#3}}}
\newcommand{\lderivativeat}[3]{\left. \frac{\partial}{\partial {#2}} {#1}
\right|_{\scriptscriptstyle {#2}={#3}}}
\newcommand{\tildephi}[1]{\widetilde{\phi}}
\newcommand{\tildePhi}[1]{\widetilde{\Phi}}
\newcommand{\tildeW}[1]{\widetilde{W}}
\newcommand{\tildeH}[1]{\widetilde{\mathcal{H}}}
\newcommand{\tildef}[1]{\widetilde{f}}
\newcommand{\tildeK}[1]{\widetilde{K}}
% \newcommand{\tildePhi}[1]{\widetilde{\Phi}_{{\scriptstyle
% \boldsymbol{\mathbf{#1}}}}}
% \newcommand{\tildephi}[1]{\widetilde{\phi}_{{\scriptstyle
% \boldsymbol{\mathbf{#1}}}}}
% \newcommand{\tildeW}[1]{\widetilde{W}_{{\scriptstyle
% \boldsymbol{\mathbf{#1}}}}}
% \newcommand{\tildef}[1]{\widetilde{f}_{{\scriptstyle
% \boldsymbol{\mathbf{#1}}}}}
% \newcommand{\tildeH}[1]{\widetilde{\mathcal{H}}_{{\scriptstyle
% \boldsymbol{\mathbf{#1}}}}}
\newcommand{\risk}[1]{\mathfrak{R}\left(#1\right)}
\newcommand{\riskemp}[1]{\mathfrak{R}_{\text{emp}}\left(#1\right)}
\let\Phi\phi
\let\phi\varphi
\DeclarePairedDelimiter\abs{\lvert}{\rvert}
\DeclarePairedDelimiter\norm{\lVert}{\rVert}
\DeclarePairedDelimiter\inner{\langle}{\rangle}
\DeclarePairedDelimiter\pairing{(}{)}
\DeclarePairedDelimiter\covariance{\text{\textbf{Cov}}_\mu[}{]}
\DeclarePairedDelimiter\covariancenomu{\text{\textbf{Cov}}[}{]}
\newcommand\dual[1]{\widehat{#1}}
% \newcommand\dual[1]{#1}
\newcommand\conj[1]{\overline{#1}}
\newcommand\inrange[2]{\in \Set{#1, \ldots, #2}}
\newcommand\converges[2]{\xrightarrow[#2]{\text{#1}}}
% \newcommand\inrange[2]{\llbracket#1, #2\rrbracket}
\makeatletter
\let\oldabs\abs
\def\abs{\@ifstar{\oldabs}{\oldabs*}}
%
\let\oldnorm\norm
\def\norm{\@ifstar{\oldnorm}{\oldnorm*}}
\makeatother
%% functions and operators
\newcommand\density{p_{\mu}}
\newcommand\measure{\mu}
\newcommand\adjoint{*}
\newcommand\transpose{\mkern-1.5mu\mathsf{T}}
\newcommand\sech{\text{sech}}
\newcommand\groupop{\star}
\newcommand\inv[1]{{#1}^{-1}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% PROOF, THEOREM, and FRIENDS
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\makeatletter
\renewtheoremstyle{plain}%
{\item[\hskip\labelsep \theorem@headerfont ##1\ ##2 \theorem@separator]}%
{\item[\hskip\labelsep \theorem@headerfont ##1\ ##2\ \theorem@separator]
{\theorem@headerfont (##3).} \theorem@separator}
\makeatother
\newtheorem{assumption}{Assumption}[chapter]
\newtheorem{remark}{Remark}[chapter]
\newtheorem{definition}{Definition}[chapter]
\theoremstyle{plain}
\newtheorem{example}{Example}[chapter]
\newtheorem{theorem}{Theorem}[chapter]
\newtheorem{lemma}{Lemma}[chapter]
\newtheorem{proposition}{Proposition}[chapter]
\newtheorem{corollary}{Corollary}[chapter]
\newtheorem{conjecture}{Conjecture}[chapter]
\newtheorem{axiom}{Axiom}[chapter]
\theoremstyle{nonumberplain}
\theoremsymbol{\ensuremath{\Box}}
\newtheorem{sproof}{Sketch of the proof}
\theoremstyle{nonumberplain}
\theoremsymbol{\ensuremath{\Box}}
\newtheorem{proof}{Proof}
\numberwithin{equation}{chapter}
\numberwithin{theorem}{chapter}