Como posso converter meu documento semelhante a este

Como posso converter meu documento semelhante a este

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\ Há poucos dias encontrei essas notas e fiquei impressionado com o estilo em que elas estão escritas. Eu também queria fazer minhas anotações (de matemática) assim.

Mas sou iniciante, em latex (no verso), então não tinha muito conhecimento de como posso converter meu documento assim. Porém, usei este site por alguns dias e de alguma forma entendi como posso escrever a seção no centro, a numeração das páginas no topo etc.

Meus códigos no preâmbulo são:

\documentclass[a4paper,twoside,english]{article}
%\usepackage[T1]{fontenc}
%\usepackage{tgtermes}
%\usepakage{times}
\usepackage[paperheight=600pt,paperwidth=515pt ,bottom=-7mm,right=22.4mm]{geometry}
\setlength{\headsep}{5mm}
%\setlength{\hoffset}{0pt}
\setlength{\oddsidemargin}{1pt}
%\setlength{\marginparwidth}{0mm}
%\setlength{\marginparsep}{0mm}
\setlength{\evensidemargin}{1pt}
\setlength{\footskip}{1.6mm}
\setlength{\voffset}{-8mm}
\setlength{\headheight}{5mm}
\setlength{\textwidth}{370pt}
\setlength{\textheight}{530pt}
%\usepackage{xcolor}
\usepackage{titlesec}
%\titleformat{\subsection}[hang]{\bfseries}{}{1em}{}
%\setcounter{secnumdepth}{1}
%\usepackage{sectsty}
%\allsectionsfont{\centering}
%\titlelabel{\thetitle . \enspace}
\renewcommand\thesection{\arabic{section}.}
\titleformat{\section}[block]{\Large\centering}{\arabic{section}.}{1em}{}
%\sectionfont{\centering}
\usepackage{fancyhdr}
\usepackage{calc}
%\usepackage{showframe}
%\usepackage{fourier}
\usepackage{graphicx} % Required for inserting images
\usepackage{blindtext}
\usepackage{amsfonts,amsmath,amssymb,amsthm}
%\renewcommand\thesubsection{\thesection.\arabic{subsection}}

Pergunta: Mas a única coisa que travei e depois de muita pesquisa não consigo descobrir é qual é o nome desses estilos de fonte e como posso carregar essas fontes no meuinteirodocumento?

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Além disso, tentei definir margens semelhantes também. Mas não consegui descobrir as margens apenas olhando o pdf.\ É possível descobrir margens semelhantes no pdf?.Se sim, como?

Qualquer ajuda será apreciada. Obrigado.

Editar:
Estou falando aqui do estilo da fonte de todo o documento. Embora à primeira vista as fontes deste pdf pareçam padrão para mim. Mas quando comparei com meu PDF escrito (em fontes padrão), isso é

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Descobri que as fontes do documento não são padrão.

Editar.2
O exemplo mínimo de trabalho é

\documentclass[a4paper,twoside,english]{article}
\usepackage{graphicx} % Required for inserting images
\usepackage[paperheight=600pt,paperwidth=515pt ,bottom=-7mm,right=22.4mm]{geometry}
\setlength{\headsep}{5mm}
\setlength{\oddsidemargin}{1pt}
\setlength{\evensidemargin}{1pt}
\setlength{\footskip}{1.6mm}
\setlength{\voffset}{-8mm}
\setlength{\headheight}{5mm}
\setlength{\textwidth}{370pt}
\setlength{\textheight}{530pt}
\usepackage{times}
\usepackage{titlesec}
\renewcommand\thesection{\arabic{section}.}
\titleformat{\section}[block]{\Large\centering\scshape}{\arabic{section}.}{1em}{}
\usepackage{fancyhdr}
\usepackage{blindtext}
\usepackage{amsfonts,amsmath,amssymb,amsthm}
\title{My doc}
\begin{document}
\section{Hello}
\blindtext
\end{document}

Editar.3
Com a ajuda e orientação do Mirco, modifiquei ligeiramente o código do Mirco e consegui o que realmente queria.
Além disso, agora sei a dimensão do pdf que é 11,33 × 14,67 pol. (retrato). Como posso emitir isso no documento?

\documentclass{amsart}

\usepackage[a4paper,margin=3.75cm, top=1.74cm,bottom=1.5cm,left=3.74cm,right=3.74cm]{geometry}
\usepackage[english]{babel}
\hyphenation{pre-image} % avoid "preim-age"

\usepackage{cleveref} % for "clever" cross-references
\usepackage{fancyhdr}
\pagestyle{fancy}
\fancyhead[C]{REAL ANALYSIS}
\fancyhead[LE,RO]{\thepage}
\fancyfoot{}
\renewcommand{\headrulewidth}{0pt}
\usepackage{blindtext}

%\usepackage{amsthm} % is loaded automatically by 'amsart' class
\theoremstyle{theorem} % italic lettering
\newtheorem{theorem}{Theorem}[section] 
\newtheorem{proposition}[theorem]{Proposition} % all theorem-like environments to share the same counter

\theoremstyle{definition} % upright lettering
\newtheorem{definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}

\theoremstyle{remark}
\newtheorem*{remark}{Remark} % 'remark' env.: not numbered

\usepackage[scr=euler]{mathalpha} % for "Euler script"

\usepackage{enumitem} % for \newlist and \setlist macros
\newlist{thmenumerate}{enumerate}{1} % 'enumerate'-like list
\setlist[thmenumerate]{label=\upshape(\alph*)} % alphabetical numbering

\crefname{thmenumeratei}{part}{parts} % label for parts of enumerated list

% -------------

\begin{document}
\section{Real Analysis}

\addtocounter{theorem}{2} % just for this example

\noindent

(earlier stuff)

\begin{definition} 
Let $(X,\mathscr{M})$ be a measurable space. A function $f\colon X\to[-\infty,\infty]$ is said to be $\mathscr{M}$-measurable (or simply \emph{measurable} when the context is clear) if the preimage 
$f^{-1}((a,\infty])=\{x\in X\colon f(x)>a\}$ is measurable for every real number~$a$.
\end{definition}

\begin{example} \phantom{.}\par % force an immediate line break
\begin{thmenumerate}
\item Constant functions are measurable.
\item Given a subset $A$ of $X$, the characteristic function $\chi_{A}$ is a measurable function if and only if $A$ is measurable.
\item The continuous functions $f\colon \mathbb{R}^d\to \mathbb{R}$ are \dots
\item The monotone functions $f\colon \mathbb{R}\to \mathbb{R}$ are \dots
\end{thmenumerate}
\end{example}

\begin{proposition} 
Let $(X,\mathscr{M})$ be a measurable space and let $f\colon X\to[-\infty,\infty]$ be a function. Then the following statements are equivalent:
\begin{thmenumerate}
\item For every real number $a$, the set \dots
\item For every real number $a$, the set \dots
\item For every real number $a$, the set \dots
\item For every real number $a$, the set \dots
\end{thmenumerate}
\end{proposition}

\begin{proposition} 
Let $(X,\mathscr{M})$ be a measurable space. If $f$ and $g$ are measurable functions defined on $X$, then the sets
\begin{thmenumerate}
\item \label{part:greaterthan} $\{x\in X\colon f(x)>g(x)\}$,
\item \label{part:greaterthanorequal} $\{x\in X\colon f(x)\ge g(x)\}$, and 
\item \label{part:equal} $\{x\in X\colon f(x)=g(x)\}$
\end{thmenumerate}
are all measurable.
\end{proposition}

\begin{proof}
If $r_1,r_2,\dots$ is an enumeration of the rational numbers, then
\[
\{x\in X : f(x)>g(x)\} =
\bigcup_{n=1}^{\infty} \bigl[x\in X: f(x)>r_n\} \cap
\{x\in X: g(x)<r_n\}\bigr] 
\]
is measurable since it is a countable union of measurable sets, establishing \cref{part:greaterthan}.

\Cref{part:greaterthanorequal} follows by noting that
\[
\{x\in X: f(x)\ge g(x)\}=\{x\in X: g(x)>f(x)\}^c,
\]
is measurable by \ref{part:greaterthan}.

Finally, to show \cref{part:equal} observe that
\[
\{x\in X:f(x)=g(x)\}=\{x\in X: f(x)\ge g(x)\} \cap 
\{x\in X: g(x)\ge f(x)\}
\]
is measurable by \ref{part:greaterthanorequal}.
\end{proof}

\begin{remark}
We now want to show that \dots
\end{remark}

\noindent
(more stuff)

\section{Measure}

\begin{definition}
By a \emph{measure} $\mu$ on a measurable space $(X,\mathscr{M})$, we mean an extended real valued nonnegative set function $\mu\colon\mathscr{M}\to[0, \infty]$ for which $\mu(\emptyset)=0$ and which is \emph{countably additive} in the sense that for any countable disjoint collection $\{E_n\}_{n=1}^{\infty}$ of measurable sets,
\[
\mu\biggl(\,\bigcup_{n=1}^{\infty} E_n \biggr) =
\sum_{n=1}^{\infty} \mu(E_n)\,.
\]
By a \emph{measure space} $(X,\mathscr{M},\mu)$ we mean a measurable space $(X,\mathscr{M})$ together with a meausure~$\mu$ defined on~$\mathscr{M}$.
\end{definition}
\blindtext
\blindtext[4]
\section{Blind}
\blindtext[4]
\section{Help}
\blindtext[4]
\end{document}

Responder1

Em vez de reinventar a roda em termos de escolha dos elementos de design de um documento, eu empregaria uma classe de documento adequada que já defina muitos dos elementos estruturais, como a formatação dos cabeçalhos das seções, do documento de interesse. Para o seu documento específico, um dos principais candidatos parece ser a amsartclasse do documento. A amsartclasse document também carrega automaticamente os pacotes amsmath, amssymbe .amsthm

E faça bom uso dos recursos dos pacotes LaTeX, como geometry(para definir parâmetros de página e margem), enumitem(para listas personalizadas do tipo enumeração, por exemplo) e cleveref(para fins de referência cruzada).

insira a descrição da imagem aqui

\documentclass{amsart}

\usepackage[a4paper,margin=3.75cm]{geometry}

\usepackage[english]{babel}
\hyphenation{pre-image} % avoid "preim-age"

\usepackage{cleveref} % for "clever" cross-references

%\usepackage{amsthm} % is loaded automatically by 'amsart' class
\theoremstyle{theorem} % italic lettering
\newtheorem{theorem}{Theorem}[section] 
\newtheorem{proposition}[theorem]{Proposition} % all theorem-like environments to share the same counter

\theoremstyle{definition} % upright lettering
\newtheorem{definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}

\theoremstyle{remark}
\newtheorem*{remark}{Remark} % 'remark' env.: not numbered

\usepackage[scr=euler]{mathalpha} % for "Euler script"

\usepackage{enumitem} % for \newlist and \setlist macros
\newlist{thmenumerate}{enumerate}{1} % 'enumerate'-like list
\setlist[thmenumerate]{label=\upshape(\alph*)} % alphabetical numbering

\crefname{thmenumeratei}{part}{parts} % label for parts of enumerated list

% -------------

\begin{document}
\section{Real Analysis}
\addtocounter{theorem}{2} % just for this example

\noindent
(earlier stuff)

\begin{definition} 
Let $(X,\mathscr{M})$ be a measurable space. A function $f\colon X\to[-\infty,\infty]$ is said to be $\mathscr{M}$-measurable (or simply \emph{measurable} when the context is clear) if the preimage 
$f^{-1}((a,\infty])=\{x\in X\colon f(x)>a\}$ is measurable for every real number~$a$.
\end{definition}

\begin{example} \phantom{.}\par % force an immediate line break
\begin{thmenumerate}
\item Constant functions are measurable.
\item Given a subset $A$ of $X$, the characteristic function $\chi_{A}$ is a measurable function if and only if $A$ is measurable.
\item The continuous functions $f\colon \mathbb{R}^d\to \mathbb{R}$ are \dots
\item The monotone functions $f\colon \mathbb{R}\to \mathbb{R}$ are \dots
\end{thmenumerate}
\end{example}

\begin{proposition} 
Let $(X,\mathscr{M})$ be a measurable space and let $f\colon X\to[-\infty,\infty]$ be a function. Then the following statements are equivalent:
\begin{thmenumerate}
\item For every real number $a$, the set \dots
\item For every real number $a$, the set \dots
\item For every real number $a$, the set \dots
\item For every real number $a$, the set \dots
\end{thmenumerate}
\end{proposition}

\begin{proposition} 
Let $(X,\mathscr{M})$ be a measurable space. If $f$ and $g$ are measurable functions defined on $X$, then the sets
\begin{thmenumerate}
\item \label{part:greaterthan} $\{x\in X\colon f(x)>g(x)\}$,
\item \label{part:greaterthanorequal} $\{x\in X\colon f(x)\ge g(x)\}$, and 
\item \label{part:equal} $\{x\in X\colon f(x)=g(x)\}$
\end{thmenumerate}
are all measurable.
\end{proposition}

\begin{proof}
If $r_1,r_2,\dots$ is an enumeration of the rational numbers, then
\[
\{x\in X : f(x)>g(x)\} =
\bigcup_{n=1}^{\infty} \bigl[x\in X: f(x)>r_n\} \cap
\{x\in X: g(x)<r_n\}\bigr] 
\]
is measurable since it is a countable union of measurable sets, establishing \cref{part:greaterthan}.

\Cref{part:greaterthanorequal} follows by noting that
\[
\{x\in X: f(x)\ge g(x)\}=\{x\in X: g(x)>f(x)\}^c,
\]
is measurable by \ref{part:greaterthan}.

Finally, to show \cref{part:equal} observe that
\[
\{x\in X:f(x)=g(x)\}=\{x\in X: f(x)\ge g(x)\} \cap 
\{x\in X: g(x)\ge f(x)\}
\]
is measurable by \ref{part:greaterthanorequal}.
\end{proof}

\begin{remark}
We now want to show that \dots
\end{remark}

\noindent
(more stuff)

\section{Measure}

\begin{definition}
By a \emph{measure} $\mu$ on a measurable space $(X,\mathscr{M})$, we mean an extended real valued nonnegative set function $\mu\colon\mathscr{M}\to[0, \infty]$ for which $\mu(\emptyset)=0$ and which is \emph{countably additive} in the sense that for any countable disjoint collection $\{E_n\}_{n=1}^{\infty}$ of measurable sets,
\[
\mu\biggl(\,\bigcup_{n=1}^{\infty} E_n \biggr) =
\sum_{n=1}^{\infty} \mu(E_n)\,.
\]
By a \emph{measure space} $(X,\mathscr{M},\mu)$ we mean a measurable space $(X,\mathscr{M})$ together with a meausure~$\mu$ defined on~$\mathscr{M}$.
\end{definition}

\end{document}

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