@ -1,26 +1,33 @@
\usepackage [top=1.5cm,bottom=1.5cm,left=1.5cm,right=1.5cm] { geometry}
\usepackage [utf8] { inputenc}
\usepackage [italian] { babel}
\usepackage { amsmath,amssymb,amsfonts,amsthm,stmaryrd}
\usepackage { amsmath}
\usepackage { amssymb}
\usepackage { amsfonts}
\usepackage { amsthm}
\usepackage { stmaryrd}
\usepackage { mathrsfs} % per mathscr
\usepackage { graphicx} % ruota freccia per le azioni
\usepackage { marvosym} % per il \Lightning
\usepackage { graphicx} % ruota freccia per le azioni
\usepackage { marvosym} % per il \Lightning
\usepackage { array}
\usepackage { faktor} % per gli insiemi quoziente
\usepackage [colorlinks=false] { hyperref}
\usepackage { xparse} % P er nuovi comandi con tanti input opzionali
\usepackage { xparse} % p er nuovi comandi con tanti input opzionali
\usepackage { relsize} % per \mathlarger
\usepackage { tikz-cd}
\usepackage { multicol}
\usepackage { multirow}
\usepackage { cancel}
\usepackage { fourier}
\usepackage { enumerate}
\usepackage { soul}
\usepackage { nicefrac}
\usepackage { longtable}
\usepackage { pdflscape}
\usepackage { mathtools}
\usepackage { lmodern}
\usepackage { accents}
\renewcommand { \vec } [1]{ { \underaccent { \bar } { { #1} } } }
\newtheorem * { warn} { \warning \; Attenzione}
@ -36,8 +43,6 @@
{ \topsep } { \topsep }
{ \normalfont } { } { \itshape } { .} { \newline } { }
\usepackage { fourier}
\theoremstyle { customth}
\newtheorem { theorem} { Teorema} [chapter]
\newtheorem { lemma} [theorem]{ Lemma}
@ -52,100 +57,57 @@
\newtheorem { notation} [theorem]{ Notazione}
\newtheorem { example} [theorem]{ Esempio}
\DeclareMathOperator { \BinNeg } { BinNeg}
\DeclareMathOperator { \Geom } { Geom}
\DeclareMathOperator { \Poisson } { Poisson}
\makeatletter
\renewenvironment { proof} [1][\proofname ]{ \par
\pushQED { \qed } %
\normalfont \topsep 6\p @\@ plus6\p @\relax
\trivlist
\item [\hskip \labelsep
\itshape
#1\@ addpunct{ .} ]\mbox { } \\ *
\itshape
#1\@ addpunct{ .} ]\mbox { } \\ *
} { %
\popQED \endtrivlist \@ endpefalse
}
\makeatother
% ============ Simboli standard =================
\newcommand { \FF } { \mathcal { F} }
\newcommand { \PP } { \mathcal { P} }
\newcommand { \NN } { \mathbb { N} }
\newcommand { \ZZ } { \mathbb { Z} }
\newcommand { \RR } { \mathbb { R} }
\newcommand { \QQ } { \mathbb { Q} }
\newcommand { \pp } { \text { p\hspace { -0.7em} \raisebox { -3.4pt} { --} } \, \, }
\newcommand { \pbern } { \pp }
\newcommand { \defeq } { \overset { \mathrm { def} } { =} }
\newcommand { \deq } { \overset { \mathrm { (d)} } { =} }
\newcommand { \toprob } { \overset { \mathbb { P} } { \to } }
\DeclareMathOperator { \VA } { VA}
\DeclareMathOperator { \im } { im}
\DeclareMathOperator { \supp } { supp}
\DeclareMathOperator { \id } { id}
\DeclareMathOperator { \sgn } { sgn}
\DeclareMathOperator { \shape } { S}
\DeclareMathOperator { \Exp } { Exp}
\DeclareMathOperator { \CI } { CI}
\newcommand { \eps } { \varepsilon }
\renewcommand { \phi } { \varphi }
\newcommand { \der } [2]{ \frac { \mathop { } \! \textnormal { \slshape d} #1} { \mathop { } \! \textnormal { \slshape d} #2} }
\newcommand { \pd } [2]{ \frac { \partial #1} { \partial #2} }
\newcommand * \dif { \mathop { } \! \textnormal { \slshape d} }
\newcommand { \dx } { \dif { x} }
\newcommand { \dy } { \dif { y} }
\newcommand { \dz } { \dif { z} }
\newcommand { \du } { \dif { u} }
\newcommand { \dv } { \dif { v} }
\newcommand { \ds } { \dif { s} }
\newcommand { \dt } { \dif { t} }
\newcommand { \dP } { \dif { P} }
\newcommand { \dm } { \dif { \mathrm { \ \! \! m} } }
% \setcounter { secnumdepth} { 1}
\newcommand { \groupto } { \rightrightarrows }
\newcommand { \restr } [2]{
#1\arrowvert _ { #2}
#1\arrowvert _ { #2}
}
\makeatletter
\def \moverlay { \mathpalette \mov @rlay}
\def \mov @rlay#1#2{ \leavevmode \vtop { %
\baselineskip \z @skip \lineskiplimit -\maxdimen
\ialign { \hfil $ \m @th# 1 ## $ \hfil \cr #2\crcr } } }
\newcommand { \charfusion } [3][\mathord ]{
#1{ \ifx #1\mathop \vphantom { #2} \fi
\mathpalette \mov @rlay{ #2\cr #3}
}
\ifx #1\mathop \expandafter \displaylimits \fi }
\makeatother
\newcommand { \cupdot } { \charfusion [\mathbin] { \cup } { \cdot } }
\newcommand { \bigcupdot } { \charfusion [\mathop] { \bigcup } { \cdot } }
\newcommand { \goesup } { \nearrow }
\newcommand { \goesdown } { \searrow }
\newcommand { \qc } { q.c.\ \! }
\newcommand { \qo } { q.o.\ \! }
\newcommand { \va } { v.a.\ \! }
\newcommand { \BB } { \mathcal { B} }
\newcommand { \EE } { \mathbb { E} }
\DeclareMathOperator { \Var } { Var}
\DeclareMathOperator { \Cov } { Cov}
\newcommand { \cS } { \mathcal { S} }
\newcommand { \inv } { ^ { -1} }
\newcommand { \abs } [1]{ \left \lvert #1 \right \rvert }
\newcommand { \norm } [1]{ \left \lVert #1 \right \rVert }
\NeedsTeXFormat { LaTeX2e}
% \ProvidesPackage { quiver} [2021/01/11 quiver]
@ -160,12 +122,12 @@
% A TikZ style for curved arrows of a fixed height, due to AndréC.
\tikzset { curve/.style={ settings={ #1} ,to path={ (\tikztostart )
.. controls ($ ( \tikztostart ) ! \pv { pos } ! ( \tikztotarget ) ! \pv { height } ! 270 : ( \tikztotarget ) $ )
and ($ ( \tikztostart ) ! 1 - \pv { pos } ! ( \tikztotarget ) ! \pv { height } ! 270 : ( \tikztotarget ) $ )
.. (\tikztotarget )\tikztonodes } } ,
settings/.code={ \tikzset { quiver/.cd,#1}
\def \pv ##1{ \pgfkeysvalueof { /tikz/quiver/##1} } } ,
quiver/.cd,pos/.initial=0.35,height/.initial=0}
.. controls ($ ( \tikztostart ) ! \pv { pos } ! ( \tikztotarget ) ! \pv { height } ! 270 : ( \tikztotarget ) $ )
and ($ ( \tikztostart ) ! 1 - \pv { pos } ! ( \tikztotarget ) ! \pv { height } ! 270 : ( \tikztotarget ) $ )
.. (\tikztotarget )\tikztonodes } } ,
settings/.code={ \tikzset { quiver/.cd,#1}
\def \pv ##1{ \pgfkeysvalueof { /tikz/quiver/##1} } } ,
quiver/.cd,pos/.initial=0.35,height/.initial=0}
% TikZ arrowhead/tail styles.
\tikzset { tail reversed/.code={ \pgfsetarrowsstart { tikzcd to} } }
