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\title{ElegantNoteï¼šä¸€ä¸ªä¼˜ç¾Žçš„ \LaTeX{} ç¬”è®°æ¨¡æ¿}

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\section{ElegantNote ä½¿ç”¨è¯´æ˜Ž}

\textbf{\textcolor{red}{æœ¬æ¨¡æ¿è‡ª 2023 å¹´ 1 æœˆ 1 æ—¥å¼€å§‹ï¼Œä¸å†ç»´æŠ¤ï¼Œä¸å»ºè®®ä½¿ç”¨æœ¬ç³»åˆ—æ¨¡æ¿ï¼ä¸ºäº†ä¿è¯ä¹‹å‰ç‰ˆæœ¬çš„ç”¨æˆ·ä»ç„¶èƒ½æŸ¥åˆ°è¯´æ˜Žæ–‡æ¡£ï¼Œæœ¬è¯´æ˜Žæ–‡æ¡£ä»ç„¶ä¿ç•™è¿‡åŽ»çš„ä¿¡æ¯ã€‚}}

æ–°ç‰ˆ ElegantNote æ˜¯åŸºäºŽæ&nbsp;‡å‡†çš„ \LaTeX{} æ–‡ç±» article é‡æ–°è®¾è®¡çš„ï¼Œæ&nbsp;¼å¼æ›´åŠ&nbsp;ç®€åŒ–çš„ç¬”è®°æ¨¡æ¿ï¼æœ¬æ¨¡æ¿æ”¯æŒä¸¤ç§ç¼–è¯‘æ–¹å¼ï¼Œ\hologo{pdfLaTeX} å’Œ \hologo{XeLaTeX}ï¼Œè‹±æ–‡æ¨¡å¼ä¸‹è¯·ä½¿ç”¨ \hologo{pdfLaTeX} è¿›è¡Œç¼–è¯‘ï¼Œä¸­æ–‡æ¨¡å¼ä¸‹åŠ¡å¿…ä½¿ç”¨ \hologo{XeLaTeX}ã€‚

æ–°æ¨¡æ¿æœ‰ä¸‹é¢å‡&nbsp;ä¸ªç‰¹æ€§ï¼š

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  \item çº¸å¼&nbsp;æ¨¡å¼ï¼šæŠ¤çœ¼æ¨¡å¼ï¼ˆgeyeï¼‰å’Œæœ¦èƒ§æ¨¡å¼ï¼ˆhazyï¼‰ï¼›
  \item é€‚é…ä¸åŒè®¾å¤‡ï¼ŒåŒ…æ‹¬ Padï¼ˆé»˜è®¤ï¼‰ï¼ŒScreenï¼ˆå¹»ç¯ç‰‡ï¼‰ï¼ŒKindleï¼ŒPCï¼ˆåŒé¡µï¼‰ï¼Œé€šç”¨ï¼ˆA4 çº¸å¼&nbsp;ï¼‰ï¼›
  \item 5 å¥—é¢œè‰²ä¸»é¢˜ï¼Œåˆ†åˆ«æ˜¯ï¼š\textcolor{eblue}{blue}ï¼ˆé»˜è®¤ï¼‰ã€\textcolor{egreen}{green}ã€\textcolor{ecyan}{cyan}ã€ \textcolor{sakura}{sakura} å’Œ \textcolor{black}{black}ï¼›
  \item è¯­è¨€æ”¯æŒï¼šä¸­æ–‡ï¼ˆé»˜è®¤ï¼‰ï¼Œè‹±æ–‡ï¼›
  \item æ”¯æŒ \hologo{pdfLaTeX} å’Œ \hologo{XeLaTeX} ç¼–è¯‘ï¼›
  \item æ›´åŠ&nbsp;ç¾Žè§‚çš„å›¾è¡¨æ&nbsp;‡é¢˜æ&nbsp;¼å¼ï¼Œåˆ—è¡¨çŽ¯å¢ƒï¼Œæ•°å­¦å­—ä½“ç­‰ï¼›
  \item å…¨å±€å­—ä½“å¤§å°æ”¯æŒï¼š8pt, 9pt, 10pt, 11pt, 12pt, 14pt, 17pt, å’Œ 20ptï¼›
  \item æ”¯æŒ \lstinline{newtx} ä»¥åŠ \lstinline{mtpro2} æ•°å­¦å­—ä½“è®¾ç½®ï¼› 
  \item ä¸­æ–‡å­—ä½“æ”¯æŒæ–¹æ­£å­—ä½“æˆ–è€…è‡ªå®šä¹‰å­—ä½“ï¼›
  \item è‹±æ–‡æ¨¡å¼é€šè¿‡ \lstinline{bibstyle} é€‰é¡¹ï¼ˆé»˜è®¤ä¸º \lstinline{apalike}ï¼‰æ”¯æŒå‚è€ƒæ–‡çŒ®æ&nbsp;¼å¼ä¿®æ”¹ï¼›
  \item æ”¯æŒå‚è€ƒæ&nbsp;¼å¼æ˜¾ç¤ºæ&nbsp;¼å¼ä¿®æ”¹ \lstinline{cite} å¯é€‰ä¸º \lstinline{authoryear}ã€\lstinline{numbers} ï¼ˆé»˜è®¤ï¼‰å’Œ \lstinline{super}ã€‚
\end{itemize}

\subsection{æ¨¡æ¿æ¨¡å¼}

æœ¬æ¨¡æ¿å¢žåŠ&nbsp;äº†æ¨¡å¼é€‰é¡¹ï¼Œåˆ†åˆ«æœ‰æŠ¤çœ¼æ¨¡å¼ï¼ˆ\lstinline{mode=geye}ï¼‰å’Œæœ¦èƒ§æ¨¡å¼ï¼ˆ\lstinline{mode=hazy}ï¼‰ã€‚å…¶ä¸­æŠ¤çœ¼æ¨¡å¼è®¾ç½®çº¸å¼&nbsp;åº•è‰²ä¸ºç»¿è±†æ²™é¢œè‰²ï¼Œè€Œæœ¦èƒ§æ¨¡å¼ä¸ºæ·¡è“è‰²ï¼Œå¼€å¯çš„æ–¹æ³•å¦‚ä¸‹ï¼š
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  \documentclass[hazy]{elegantnote} % or
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\begin{remark}
  å¦‚æžœä½&nbsp;æƒ³ä¸ºè‡ªå·±çš„æ–‡æ¡£æ·»åŠ&nbsp;åº•è‰²ï¼Œå¯ä»¥åœ¨å¯¼è¨€åŒºæ·»åŠ&nbsp;ä¸‹é¢è®¾ç½®ï¼š
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\subsection{è®¾å¤‡é€‰æ‹©}

ä¸ºäº†è®©ç¬”è®°æ–¹ä¾¿åœ¨ä¸åŒè®¾å¤‡ä¸Šé˜…è¯»ï¼Œå…åŽ»åˆ‡è¾¹ï¼Œç¼©æ”¾ç­‰æ“ä½œï¼Œæœ¬æ¨¡æ¿é€‚é…ä¸åŒçš„è®¾å¤‡ï¼Œåˆ†åˆ«ä¸º Padï¼ˆé»˜è®¤ï¼‰ï¼ŒKindleï¼ŒPCï¼ŒA4ã€‚

\textcolor{red}{\kaishu æ–°å¢ž}ï¼šä¸ºäº†æ–¹ä¾¿å±•ç¤ºç¬”è®°ï¼Œ2.20 ç‰ˆæœ¬æ–°å¢žäº† \lstinline{device=screen} è®¾å¤‡é€‰é¡¹ï¼Œå¤§å°ä¸º MS Powerpoint çš„çº¸å¼&nbsp;å¤§å°ï¼Œæ¯”ä¾‹ä¸º 4:3ï¼ˆ2019/12/06ï¼‰ã€‚

ä¸åŒå±å¹•çš„é€‰æ‹©ä¸º
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  \documentclass[device=normal]{elegantnote} % a4 normal page
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\begin{note}
ä¹Ÿå¯ä»¥é‡‡å–ç›´æŽ¥èµ‹å€¼çš„æ–¹æ³•é€‰æ‹©å±å¹•ï¼Œæ¯”å¦‚ï¼š
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\begin{note}
  å¦‚æžœæƒ³è¦æ­£å¸¸çš„ A4 å¤§å°çš„ PDFï¼Œéœ€è¦é€‰æ‹© \lstinline{device=normal}ã€‚
\end{note}


\subsection{æ•°å­¦å­—ä½“é€‰é¡¹}

æœ¬æ¨¡æ¿å®šä¹‰äº†ä¸€ä¸ªæ•°å­¦å­—ä½“é€‰é¡¹ï¼ˆ\lstinline{math}ï¼‰ï¼Œå¯é€‰é¡¹æœ‰ä¸‰ä¸ªï¼š
\begin{enumerate}
  \item \lstinline{math=cm}ï¼ˆé»˜è®¤ï¼‰ï¼Œä½¿ç”¨ \LaTeX{} é»˜è®¤æ•°å­¦å­—ä½“ï¼ˆæŽ¨èï¼Œæ—&nbsp;éœ€å£°æ˜Žï¼‰ï¼›
  \item \lstinline{math=newtx}ï¼Œä½¿ç”¨ \lstinline{newtxmath} è®¾ç½®æ•°å­¦å­—ä½“ï¼ˆæ½œåœ¨é—®é¢˜æ¯”è¾ƒå¤šï¼‰ã€‚
  \item \lstinline{math=mtpro2}ï¼Œä½¿ç”¨ \lstinline{mtpro2} å®åŒ…è®¾ç½®æ•°å­¦å­—ä½“ï¼Œè¦æ±‚ç”¨æˆ·å·²ç»æˆåŠŸå®‰è£…æ­¤å®åŒ…ã€‚
\end{enumerate}


\subsection{ä¸­æ–‡å­—ä½“é€‰é¡¹}
æ¨¡æ¿æä¾›ä¸­æ–‡å­—ä½“é€‰é¡¹ \lstinline{chinesefont}ï¼Œå¯é€‰é¡¹æœ‰
\begin{enumerate}
\item \lstinline{ctexfont}ï¼šé»˜è®¤é€‰é¡¹ï¼Œä½¿ç”¨ \lstinline{ctex} å®åŒ…æ&nbsp;¹æ®ç³»ç»Ÿè‡ªè¡Œé€‰æ‹©å­—ä½“ï¼Œå¯èƒ½å­˜åœ¨å­—ä½“ç¼ºå¤±çš„é—®é¢˜ï¼Œæ›´å¤šå†…å®¹å‚è€ƒ \lstinline{ctex} å®åŒ…\href{https://ctan.org/pkg/ctex}{å®˜æ–¹æ–‡æ¡£}\footnote{å¯ä»¥ä½¿ç”¨å‘½ä»¤æç¤ºç¬¦ï¼Œè¾“å…¥ \lstinline{texdoc ctex} è°ƒå‡ºæœ¬åœ° \lstinline{ctex} å®åŒ…æ–‡æ¡£}ã€‚
\item \lstinline{founder}ï¼šæ–¹æ­£å­—ä½“é€‰é¡¹ï¼ˆéœ€è¦ç”¨æˆ·å®‰è£…å­—ä½“ï¼‰ï¼Œè°ƒç”¨ \lstinline{ctex} å®åŒ…å¹¶ä¸”ä½¿ç”¨ \lstinline{fontset=none} é€‰é¡¹ï¼Œç„¶åŽè®¾ç½®å­—ä½“ä¸ºæ–¹æ­£å››æ¬¾å…è´¹å­—ä½“ï¼Œæ–¹æ­£å­—ä½“ä¸‹è½½æ³¨æ„äº‹é¡¹è§åŽæ–‡ã€‚
\item \lstinline{nofont}ï¼šè°ƒç”¨ \lstinline{ctex} å®åŒ…å¹¶ä¸”ä½¿ç”¨ \lstinline{fontset=none} é€‰é¡¹ï¼Œä¸è®¾å®šä¸­æ–‡å­—ä½“ï¼Œç”¨æˆ·å¯ä»¥è‡ªè¡Œè®¾ç½®ä¸­æ–‡å­—ä½“ï¼Œå…·ä½“è§åŽæ–‡ã€‚
\end{enumerate}

\noindent \textbf{æ³¨æ„ï¼š} ä½¿ç”¨ \lstinline{founder} é€‰é¡¹æˆ–è€… \lstinline{nofont} æ—¶ï¼Œå¿…é¡»ä½¿ç”¨ \hologo{XeLaTeX} è¿›è¡Œç¼–è¯‘ã€‚

\subsubsection{æ–¹æ­£å­—ä½“é€‰é¡¹}
ç”±äºŽä½¿ç”¨ \lstinline{ctex} å®åŒ…é»˜è®¤è°ƒç”¨ç³»ç»Ÿå·²æœ‰çš„å­—ä½“ï¼Œéƒ¨åˆ†ç³»ç»Ÿå­—ä½“ç¼ºå¤±ä¸¥é‡ï¼Œå›&nbsp;æ­¤ï¼Œç”¨æˆ·å¸Œæœ›èƒ½å¤Ÿä½¿ç”¨å…¶å®ƒå­—ä½“ï¼Œæˆ‘ä»¬æŽ¨èä½¿ç”¨æ–¹æ­£å­—ä½“ã€‚æ–¹æ­£çš„{\songti æ–¹æ­£ä¹¦å®‹}ã€{\heiti æ–¹æ­£é»‘ä½“}ã€{\kaishu æ–¹æ­£æ¥·ä½“}ã€{\fangsong æ–¹æ­£ä»¿å®‹}å››æ¬¾å­—ä½“å‡å¯å…è´¹è¯•ç”¨ï¼Œä¸”å¯ç”¨äºŽå•†ä¸šç”¨é€”ã€‚ç”¨æˆ·å¯ä»¥è‡ªè¡Œä»Ž\href{http://www.foundertype.com/}{æ–¹æ­£å­—ä½“å®˜ç½‘}ä¸‹è½½æ­¤å››æ¬¾å­—ä½“ï¼Œåœ¨ä¸‹è½½çš„æ—¶å€™è¯·\textbf{åŠ¡å¿…}æ³¨æ„é€‰æ‹© GBK å­—ç¬¦é›†ï¼Œä¹Ÿå¯ä»¥ä½¿ç”¨ \href{https://www.latexstudio.net/}{\LaTeX{} å·¥ä½œå®¤}æä¾›çš„\href{https://pan.baidu.com/s/1BgbQM7LoinY7m8yeP25Y7Q}{æ–¹æ­£å­—ä½“ï¼Œæå–ç&nbsp;ä¸ºï¼šnjy9} è¿›è¡Œå®‰è£…ã€‚å®‰è£…æ—¶ï¼Œ{\kaishu Win 10 ç”¨æˆ·è¯·å³é”®é€‰æ‹©ä¸ºå…¨éƒ¨ç”¨æˆ·å®‰è£…ï¼Œå¦åˆ™ä¼šæ‰¾ä¸åˆ°å­—ä½“ã€‚}

\begin{figure}[!htb]
\centering
\includegraphics[width=0.9\textwidth]{founder.png}
\end{figure}

\subsubsection{å…¶ä»–ä¸­æ–‡å­—ä½“}
å¦‚æžœä½&nbsp;æƒ³å®Œå…¨è‡ªå®šä¹‰å­—ä½“\footnote{è¿™é‡Œä»ç„¶ä»¥æ–¹æ­£å­—ä½“ä¸ºä¾‹ã€‚}ï¼Œä½&nbsp;å¯ä»¥é€‰æ‹© \lstinline{chinesefont=nofont}ï¼Œç„¶åŽåœ¨å¯¼è¨€åŒºè®¾ç½®ï¼Œå‚è€ƒä»£ç&nbsp;å¦‚ä¸‹ï¼š
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  \setCJKsansfont[BoldFont={FZHei-B01}]{FZKai-Z03}
  \setCJKmonofont[BoldFont={FZHei-B01}]{FZFangSong-Z02}
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  \newcommand*{\heiti}{\CJKfamily{zhhei}}
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  \newcommand*{\fangsong}{\CJKfamily{zhfs}}
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\subsection[é¢œè‰²ä¸»é¢˜]{é¢œè‰²ä¸»é¢˜\footnote{æµ‹è¯•ç«&nbsp;èŠ‚è„šæ³¨ã€‚}}

æœ¬æ¨¡æ¿å†…ç½® 5 å¥—é¢œè‰²ä¸»é¢˜ï¼Œåˆ†åˆ«æ˜¯ \textcolor{eblue}{blue}ï¼ˆé»˜è®¤ï¼‰ï¼Œ\textcolor{egreen}{green}ï¼Œ \textcolor{ecyan}{cyan}ï¼Œ \textcolor{sakura}{sakura} å’Œ \textcolor{black}{black}ã€‚å¦‚æžœä¸éœ€è¦é¢œè‰²ï¼Œå¯ä»¥é€‰æ‹©é»‘è‰²ï¼ˆblackï¼‰ä¸»é¢˜ã€‚é¢œè‰²ä¸»é¢˜çš„è®¾ç½®æ–¹æ³•ï¼š
\begin{lstlisting}[frame=none]  
  \documentclass[green]{elegantnote}
  \documentclass[color=green]{elegantnote}
  ...
  \documentclass[black]{elegantnote}
  \documentclass[color=black]{elegantnote}
\end{lstlisting}


\subsection{è¯­è¨€æ¨¡å¼}

æœ¬æ¨¡æ¿å†…å«ä¸¤å¥—è¯­è¨€çŽ¯å¢ƒï¼Œæ”¹å˜è¯­è¨€çŽ¯å¢ƒä¼šæ”¹å˜å›¾è¡¨æ&nbsp;‡é¢˜çš„å¼•å¯¼è¯ï¼ˆå›¾ï¼Œè¡¨ï¼‰ï¼Œæ–‡ç«&nbsp;ç»“æž„è¯ï¼ˆæ¯”å¦‚ç›®å½•ï¼Œå‚è€ƒæ–‡çŒ®ç­‰ï¼‰ï¼Œä»¥åŠå®šç†çŽ¯å¢ƒä¸­çš„å¼•å¯¼è¯ï¼ˆæ¯”å¦‚å®šç†ï¼Œå¼•ç†ç­‰ï¼‰ã€‚ä¸åŒè¯­è¨€æ¨¡å¼çš„å¯ç”¨å¦‚ä¸‹ï¼š
\begin{lstlisting}[frame=none]  
  \documentclass[cn]{elegantnote} 
  \documentclass[lang=cn]{elegantnote} 
  \documentclass[en]{elegantnote} 
  \documentclass[lang=en]{elegantnote}
\end{lstlisting}

\begin{note}
åªæœ‰ä¸­æ–‡æ¨¡å¼æ‰å¯è¾“å…¥ä¸­æ–‡ï¼Œå¦‚æžœéœ€è¦åœ¨è‹±æ–‡æ¨¡å¼ä¸‹è¾“å…¥ä¸­æ–‡ï¼Œå¯ä»¥è‡ªè¡Œæ·»åŠ&nbsp; \lstinline{ctex} å®åŒ…\footnote{éœ€è¦ä½¿ç”¨ \lstinline{scheme=plain} é€‰é¡¹æ‰ä¸ä¼šæŠŠæ&nbsp;‡é¢˜æ”¹ä¸ºä¸­æ–‡ã€‚}æˆ–è€…ä½¿ç”¨ \lstinline{xeCJK} å®åŒ…è®¾ç½®å­—ä½“ã€‚å¦å¤–å¦‚æžœåœ¨ç¬”è®°ä¸­ä½¿ç”¨äº†æŠ„å½•çŽ¯å¢ƒï¼ˆ\lstinline{lstlisting}ï¼‰ï¼Œå¹¶ä¸”é‡Œé¢æœ‰ä¸­æ–‡å­—ç¬¦ï¼Œè¯·åŠ¡å¿…ä½¿ç”¨ \hologo{XeLaTeX} ç¼–è¯‘ã€‚
\end{note}


\subsection{å®šç†ç±»çŽ¯å¢ƒ}

æ­¤æ¨¡æ¿é‡‡ç”¨äº† \lstinline{amsthm} ä¸­çš„å®šç†æ&nbsp;·å¼ï¼Œä½¿ç”¨äº† 4 ç±»å®šç†æ&nbsp;·å¼ï¼Œæ‰€åŒ…å«çš„çŽ¯å¢ƒåˆ†åˆ«ä¸º
\begin{itemize}
  \item \textbf{å®šç†ç±»}ï¼štheoremï¼Œlemmaï¼Œpropositionï¼Œcorollaryï¼›
  \item \textbf{å®šä¹‰ç±»}ï¼šdefinitionï¼Œconjectureï¼Œexampleï¼›
  \item \textbf{å¤‡æ³¨ç±»}ï¼šremarkï¼Œnoteï¼Œcaseï¼›
  \item \textbf{è¯æ˜Žç±»}ï¼šproofã€‚
\end{itemize}

\begin{remark}
åœ¨é€‰ç”¨ \lstinline{lang=cn} æ—¶ï¼Œå®šç†ç±»çŽ¯å¢ƒçš„å¼•å¯¼è¯å…¨éƒ¨ä¼šæ”¹ä¸ºä¸­æ–‡ã€‚
\end{remark}


\section{å†™ä½œç¤ºä¾‹}

æˆ‘ä»¬å°†é€šè¿‡ä¸‰ä¸ªæ­¥éª¤å®šä¹‰å¯æµ‹å‡½æ•°çš„ç§¯åˆ†ã€‚é¦–å…ˆå®šä¹‰éžè´Ÿç®€å•å‡½æ•°çš„ç§¯åˆ†ã€‚ä»¥ä¸‹è®¾ $E$ æ˜¯ $\mathcal{R}^n$ ä¸­çš„å¯æµ‹é›†ã€‚

\begin{definition}[å¯ç§¯æ€§]
è®¾ $ f(x)=\sum\limits_{i=1}^{k} a_i \chi_{A_i}(x)$ æ˜¯ $E$ ä¸Šçš„éžè´Ÿç®€å•å‡½æ•°ï¼Œå…¶ä¸­ $\{A_1,A_2,\ldots$, $A_k\}$ æ˜¯ $E$ ä¸Šçš„ä¸€ä¸ªå¯æµ‹åˆ†å‰²ï¼Œ$a_1,a_2,\ldots,a_k$ æ˜¯éžè´Ÿå®žæ•°ã€‚å®šä¹‰ $f$ åœ¨ $E$ ä¸Šçš„ç§¯åˆ†ä¸º 1. 3
\begin{equation}
   \label{inter}
   \int_{E} f dx = \sum_{i=1}^k a_i m(A_i).
\end{equation}
ä¸€èˆ¬æƒ…å†µä¸‹ $0 \leq \int_{E} f dx \leq \infty$ã€‚è‹¥ $\int_{E} f dx &lt; \infty$ï¼Œåˆ™ç§° $f$ åœ¨ $E$ ä¸Šå¯ç§¯ã€‚
\end{definition}

ä¸€ä¸ªè‡ªç„¶çš„é—®é¢˜æ˜¯ï¼ŒLebesgue ç§¯åˆ†ä¸Žæˆ‘ä»¬æ‰€ç†Ÿæ‚‰çš„ Riemann ç§¯åˆ†æœ‰ä»€ä¹ˆè”ç³»å’ŒåŒºåˆ«ï¼Ÿä¹‹åŽæˆ‘ä»¬å°†è¯¦ç»†è®¨è®º Riemann ç§¯åˆ†ä¸Ž Lebesgue ç§¯åˆ†çš„å…³ç³»ã€‚è¿™é‡Œåªçœ‹ä¸€ä¸ªç®€å•çš„ä¾‹å­ã€‚è®¾ $D(x)$ æ˜¯åŒºé—´ $[0,1]$ ä¸Šçš„ Dirichlet å‡½æ•°ã€‚å³ $D(x)=\chi_{Q_0}(x)$ï¼Œå…¶ä¸­ $Q_0$ è¡¨ç¤º $[0,1]$ ä¸­çš„æœ‰ç†æ•°çš„å…¨ä½“ã€‚æ&nbsp;¹æ®éžè´Ÿç®€å•å‡½æ•°ç§¯åˆ†çš„å®šä¹‰ï¼Œ$D(x)$ åœ¨ $[0,1]$ ä¸Šçš„ Lebesgue ç§¯åˆ†ä¸º
\begin{equation}\label{inter2}
  \int_0^1 D(x)dx = \int_0^1 \chi_{Q_0} (x) dx = m(Q_0) = 0
\end{equation}
å³ $D(x)$ åœ¨ $[0,1]$ ä¸Šæ˜¯ Lebesgue å¯ç§¯çš„å¹¶ä¸”ç§¯åˆ†å€¼ä¸ºé›¶ã€‚ä½† $D(x)$ åœ¨ $[0,1]$ ä¸Šä¸æ˜¯ Riemann å¯ç§¯çš„ã€‚

\begin{table}[htbp]
  \centering
  \small
  \caption{ç‡ƒæ²¹æ•ˆçŽ‡ä¸Žæ±½è½¦ä»·æ&nbsp;¼}
    \begin{tabular}{lcc}
    \toprule
                  &amp;       (1)         &amp;        (2)      \\
    \midrule
    ç‡ƒæ²¹æ•ˆçŽ‡      &amp;   -238.90***      &amp;      -49.51     \\
                  &amp;    (53.08)        &amp;      (86.16)    \\
    æ±½è½¦é‡é‡      &amp;                   &amp;        1.75***  \\
                  &amp;                   &amp;       (0.641)   \\
    å¸¸æ•°é¡¹        &amp;  11253.00***      &amp;    1946.00      \\
                  &amp;  (1171.00)        &amp;   (3597.00)     \\
    è§‚æµ‹æ•°        &amp;     74            &amp;      74         \\
    $R^2$         &amp;      0.220        &amp;       0.293     \\
    \bottomrule
    \end{tabular}%
  \label{tab:reg}%
\end{table}%

\begin{theorem}[Fubini å®šç†]\label{thm:fubi}
è‹¥ $f(x,y)$ æ˜¯ $\mathcal{R}^p\times\mathcal{R}^q$ ä¸Šçš„éžè´Ÿå¯æµ‹å‡½æ•°ï¼Œåˆ™å¯¹å‡&nbsp;ä¹Žå¤„å¤„çš„ $x\in \mathcal{R}^p$ï¼Œ$f(x,y)$ ä½œä¸º $y$ çš„å‡½æ•°æ˜¯ $\mathcal{R}^q$ ä¸Šçš„éžè´Ÿå¯æµ‹å‡½æ•°ï¼Œ$g(x)=\int_{\mathcal{R}^q}f(x,y) dy$ æ˜¯ $\mathcal{R}^p$ ä¸Šçš„éžè´Ÿå¯æµ‹å‡½æ•°ã€‚å¹¶ä¸”
\begin{equation}\label{eq:461}
  \int_{\mathcal{R}^p\times\mathcal{R}^q} f(x,y) dxdy=\int_{\mathcal{R}^p}\left(\int_{\mathcal{R}^q}f(x,y)dy\right)dx.
\end{equation}
\end{theorem}

\begin{proof}
Let $z$ be some element of $xH \cap yH$.  Then $z = xa$ for some $a \in H$, and $z = yb$ for some $b \in H$. If $h$ is any element of $H$ then $ah \in H$ and $a^{-1}h \in H$, since $H$ is a subgroup of $G$. But $zh = x(ah)$ and $xh = z(a^{-1}h)$ for all $h \in H$. Therefore $zH \subset xH$ and $xH \subset zH$, and thus $xH = zH$.  Similarly $yH = zH$, and thus $xH = yH$, as required.
\end{proof}


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%\printbibliography[heading=bibintoc, title=\ebibname]

\end{document}
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