Как мне преобразовать мой документ в аналогичный этому?

Question

Вместо того, чтобы изобретать велосипед в плане выбора элементов дизайна документа, я бы использовал подходящий класс документа, который уже определяет многие структурные элементы, такие как форматирование заголовков разделов, интересующего документа. Для вашего конкретного документа одним из ведущих кандидатов, по-видимому, будет amsartкласс документа. amsartКласс документа также автоматически загружает пакеты amsmath, amssymbи amsthm.

И постарайтесь эффективно использовать возможности пакетов LaTeX, например geometry(для установки параметров страницы и полей), enumitem(например, для создания списков, подобных перечислимым) и cleveref(для перекрестных ссылок).

\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}

Answer 1

Вместо того, чтобы изобретать велосипед в плане выбора элементов дизайна документа, я бы использовал подходящий класс документа, который уже определяет многие структурные элементы, такие как форматирование заголовков разделов, интересующего документа. Для вашего конкретного документа одним из ведущих кандидатов, по-видимому, будет amsartкласс документа. amsartКласс документа также автоматически загружает пакеты amsmath, amssymbи amsthm.

И постарайтесь эффективно использовать возможности пакетов LaTeX, например geometry(для установки параметров страницы и полей), enumitem(например, для создания списков, подобных перечислимым) и cleveref(для перекрестных ссылок).

\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}

Как мне преобразовать мой документ в аналогичный этому?

решение1

Связанный контент