% Various theorem-type declarations
\newtheorem{thm}{Theorem}[section]
\newtheorem{lem}[thm]{Lemma}
\newtheorem{cor}[thm]{Corollary}
\newtheorem{prop}[thm]{Proposition}

\theoremstyle{definition}
\newtheorem{eg}[thm]{Example}
\newtheorem{defn}[thm]{Definition}
\newtheorem{rem}[thm]{Remark}

% Ignore a block of text
\newcommand{\commentout}[1]{}

% Make a side comment
\newcommand{\mpar}[1]{\marginpar{\tiny{#1}}}

% self map
\newcommand{\self}{\circlearrowleft}

% Generic math macros

% Area
\newcommand{\Area}{\mathrm{Area}\,}

%
\newcommand{\volume}{\mathrm{Vol}\,}

% Set of points within distance #2 of set #1
\newcommand{\ball}[2]{B_{#1}(#2)}

% Boundary 
\newcommand{\bdry}{\partial}

% Interior
\newcommand{\interior}{\mathrm{int}\,}

% Domain and range
\newcommand{\dom}{\text{dom}}
\newcommand{\ran}{\text{ran}}

% Cardinality
\newcommand{\card}{\#}

% Multiplicity
\newcommand{\mult}{\nu}

% The d-bar operator
\newcommand{\dbar}{\overline\partial}

% Unit disk 
\newcommand{\disk}{\Delta}

% Distance between two points or sets
\newcommand{\dist}{\mathrm{dist}}

% Equal to by definition
\newcommand{\eqdef}{\stackrel{\mathrm{def}}{=}}

% Identity map
\newcommand{\id}{\mathrm{id}}

% L^1 loc
\newcommand{\lol}{L^1_{loc}}

% Lelong number of a current at a point
\newcommand{\lelong}{\nu}

% Matrix groups and algebras
\newcommand{\GL}[2]{GL(#1,#2)}

% Except for the origin
\newcommand{\minuso}{\setminus\{\origin\}}

% The #1 norm of #2
\newcommand{\norm}[2][{}]{\left\|#2\right\|_{#1}}

% The origin
\newcommand{\origin}{\mathbf{0}}

% Pair a linear functional with a vector
\newcommand{\pair}[2]{\langle #1,#2 \rangle}

% Various number fields
\newcommand{\R}{\mathbf{R}}
\newcommand{\uscr}{\mathbf{R}\cup\{-\infty\}}
\newcommand{\C}{\mathbf{C}}
\newcommand{\cp}{\mathbf{P}}
\newcommand{\Z}{\mathbf{Z}}
\newcommand{\N}{\mathbf{N}}
\newcommand{\zp}{\mathbf{Z}}
\newcommand{\cstar}{\mathbf{C}^*}

% Mass of a current
\newcommand{\mass}[2][{}]{\mathrm{M}_{#1}[#2]}

% Support 
\newcommand{\supp}{\mathrm{supp}\,}

% Tangent space (at a point #1)
\newcommand{\tanspace}[1][{}]{\mathrm{T}_{#1}}




