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如何对线做出例外处理，以便它可以延伸出边距

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如何对线做出例外处理，以便它可以延伸出边距

在下面的例子中，是否可以对花括号右侧的不等式宽容一些，以便它（并且只有那部分）可以延伸到边距之外？（这样，左侧的编号和等式都可以在同一行中）

\documentclass[leqno,10pt]{article}
\usepackage{soul}
\usepackage[margin=0.75in]{geometry}
\def\changemargin#1#2{\list{}{\rightmargin#2\leftmargin#1}\item[]}
\let\endchangemargin=\endlist 
\usepackage{fancyhdr}
\pagestyle{fancy}
\lhead{Lecture 1}
\rhead{Handout 3}
\usepackage{mathtools}
\usepackage{enumitem,array}
\usepackage{relsize}
\usepackage{amsmath}
\usepackage{amsthm} %for proof 
\newtheorem*{mythm}{Theorem}
\newtheorem*{mydef}{Definition}
\newtheorem*{mycases}{Special Cases}
\title{\ul{Conditional Expectations in Bivariate Probability Distribution}}
\date{}
\newenvironment{mydescription}{%
   \renewcommand\descriptionlabel[1]{\hspace{\labelsep}\textbf{{##1}}}%
   \begin{description}%
}{%
   \end{description}%
}
\newenvironment{definition}[1][Definition]{\begin{trivlist}
\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}

\providecommand\given{} 
\DeclarePairedDelimiterX{\EV}[1]{E(}{)}{\renewcommand\given{\nonscript\,\delimsize\vert\nonscript\,} #1}
\providecommand\iven{} 
\DeclarePairedDelimiterX{\V}[1]{V(}{)}{\renewcommand\iven{\nonscript\,\delimsize\vert\nonscript\,} #1}

\begin{document}

\newenvironment{Myitemize}{%
\renewcommand{\labelitemi}{{}}%
\begin{itemize}[nosep]}{\end{itemize}}

\maketitle

\newcommand{\myitem}{\stepcounter{enumi}\item[(\theenumi)]}%for enumerate with no. in brackets
\newcommand\litem[1]{\item{\bfseries {#1}}}

\thispagestyle{fancy}

\begin{mydef} 
If the random vector $(X,Y)$ has joint \textbf{pdf} $f(x,y)$ with conditional \textbf{pdf} $g_{2}(y|x)$, and if $Z=h(X,Y)$ is a (single-valued) function of (X,Y). Then the conditional expectation of the random variable $Z$, given $X=x$ is 
\begin{equation}
E(Z|x)=\int_{-\infty}^{\infty}{h(x,y)g_{2}(y|x)dy}
\label{eq:}
\end{equation}
\end{mydef} 

\begin{mycases}
(a,b,c are constants; ($X^{*}=X-E(X); Y^{*}=Y-E(Y)$)\\
\begin{flalign}\label{cas}
    & Z=a+bX+cY & \Rightarrow\quad & \!\begin{aligned}[t]\EV{Z \given x}&=\EV{a \given x}+b.\EV{X \given x}+c.\EV{Y \given x} \\&= a+bx+c.\EV{Y \given x} \end{aligned} &\hphantom{Z=a+bX+cY\quad(2)} & \\
   & Z=XY & \Rightarrow\quad & \EV{Z \given x} = x\EV{Y \given x}\\
 & Z = Y & \Rightarrow\quad & \EV{Z \given x} = \EV{Y \given x} = \mu_{Y|x} = \text{The CE of Y given X}\\
 & Z=(Y-\mu_{Y|X})^{2} &\Rightarrow\quad & \EV{Z \given x} = \V{Y \iven x} = \sigma^{2}_{Y|x}=\text{The CV of Y given X}
\smash{\raisebox{-10pt}{$\left.\rule{0pt}{17pt}\right\} \EV{(Y-\mu_{Y|X})^{2} \given X}\leq \EV{Y-\mu_{Y})^{2} \given X}$}}\\
 & Z=(Y-\mu_{Y})^{2} & \Rightarrow\quad & \EV{Z \given x} = \V{Y \iven x} + (\mu_{Y|x}-\mu_{Y})^2
\end{flalign}

\end{mycases}

\end{document}

答案1

这符合您的要求，但您可以考虑另一种方法，因为它会推到纸张边缘。尽管如此，我对您的 MWE 做了两件事。首先，我将 包裹\smash{}在 中\rlap，如\rlap{\smash{}}。这具有忽略 参数\rlap从当前位置向右重叠时占用的水平空间的效果（因此它可以防止 LaTeX 检测到相关的边距超限）。我还在\!括号后插入了一个小的负空间，以尝试在右边距提供一些缓解。

\documentclass[leqno,10pt]{article}
\usepackage{soul}
\usepackage[margin=0.75in]{geometry}
\def\changemargin#1#2{\list{}{\rightmargin#2\leftmargin#1}\item[]}
\let\endchangemargin=\endlist 
\usepackage{fancyhdr}
\pagestyle{fancy}
\lhead{Lecture 1}
\rhead{Handout 3}
\usepackage{mathtools}
\usepackage{enumitem,array}
\usepackage{relsize}
\usepackage{amsmath}
\usepackage{amsthm} %for proof 
\newtheorem*{mythm}{Theorem}
\newtheorem*{mydef}{Definition}
\newtheorem*{mycases}{Special Cases}
\title{\ul{Conditional Expectations in Bivariate Probability Distribution}}
\date{}
\newenvironment{mydescription}{%
   \renewcommand\descriptionlabel[1]{\hspace{\labelsep}\textbf{{##1}}}%
   \begin{description}%
}{%
   \end{description}%
}
\newenvironment{definition}[1][Definition]{\begin{trivlist}
\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}

\providecommand\given{} 
\DeclarePairedDelimiterX{\EV}[1]{E(}{)}{\renewcommand\given{\nonscript\,\delimsize\vert\nonscript\,} #1}
\providecommand\iven{} 
\DeclarePairedDelimiterX{\V}[1]{V(}{)}{\renewcommand\iven{\nonscript\,\delimsize\vert\nonscript\,} #1}

\begin{document}

\newenvironment{Myitemize}{%
\renewcommand{\labelitemi}{{}}%
\begin{itemize}[nosep]}{\end{itemize}}

\maketitle

\newcommand{\myitem}{\stepcounter{enumi}\item[(\theenumi)]}%for enumerate with no. in brackets
\newcommand\litem[1]{\item{\bfseries {#1}}}

\thispagestyle{fancy}

\begin{mydef} 
If the random vector $(X,Y)$ has joint \textbf{pdf} $f(x,y)$ with conditional \textbf{pdf} $g_{2}(y|x)$, and if $Z=h(X,Y)$ is a (single-valued) function of (X,Y). Then the conditional expectation of the random variable $Z$, given $X=x$ is 
\begin{equation}
E(Z|x)=\int_{-\infty}^{\infty}{h(x,y)g_{2}(y|x)dy}
\label{eq:}
\end{equation}
\end{mydef} 

\begin{mycases}
(a,b,c are constants; ($X^{*}=X-E(X); Y^{*}=Y-E(Y)$)\\
\begin{flalign}\label{cas}
    & Z=a+bX+cY & \Rightarrow\quad & \!\begin{aligned}[t]\EV{Z \given x}&=\EV{a \given x}+b.\EV{X \given x}+c.\EV{Y \given x} \\&= a+bx+c.\EV{Y \given x} \end{aligned} &\hphantom{Z=a+bX+cY\quad(2)} & \\
   & Z=XY & \Rightarrow\quad & \EV{Z \given x} = x\EV{Y \given x}\\
 & Z = Y & \Rightarrow\quad & \EV{Z \given x} = \EV{Y \given x} = \mu_{Y|x} = \text{The CE of Y given X}\\
 & Z=(Y-\mu_{Y|X})^{2} &\Rightarrow\quad & \EV{Z \given x} = \V{Y \iven x} = \sigma^{2}_{Y|x}=\text{The CV of Y given X}
\rlap{\smash{\raisebox{-10pt}{$\left.\rule{0pt}{17pt}\right\}\!\EV{(Y-\mu_{Y|X})^{2} \given X}\leq \EV{Y-\mu_{Y})^{2} \given X}$}}}\\
 & Z=(Y-\mu_{Y})^{2} & \Rightarrow\quad & \EV{Z \given x} = \V{Y \iven x} + (\mu_{Y|x}-\mu_{Y})^2
\end{flalign}

\end{mycases}

\end{document}

在此处输入图片描述

以下是使用堆栈的替代方法，它遵循边距：

\documentclass[leqno,10pt]{article}
\usepackage{soul}
\usepackage[margin=0.75in]{geometry}
\usepackage{stackengine}
\stackMath
\def\changemargin#1#2{\list{}{\rightmargin#2\leftmargin#1}\item[]}
\let\endchangemargin=\endlist 
\usepackage{fancyhdr}
\pagestyle{fancy}
\lhead{Lecture 1}
\rhead{Handout 3}
\usepackage{mathtools}
\usepackage{enumitem,array}
\usepackage{relsize}
\usepackage{amsmath}
\usepackage{amsthm} %for proof 
\newtheorem*{mythm}{Theorem}
\newtheorem*{mydef}{Definition}
\newtheorem*{mycases}{Special Cases}
\title{\ul{Conditional Expectations in Bivariate Probability Distribution}}
\date{}
\newenvironment{mydescription}{%
   \renewcommand\descriptionlabel[1]{\hspace{\labelsep}\textbf{{##1}}}%
   \begin{description}%
}{%
   \end{description}%
}
\newenvironment{definition}[1][Definition]{\begin{trivlist}
\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}

\providecommand\given{} 
\DeclarePairedDelimiterX{\EV}[1]{E(}{)}{\renewcommand\given{\nonscript\,\delimsize\vert\nonscript\,} #1}
\providecommand\iven{} 
\DeclarePairedDelimiterX{\V}[1]{V(}{)}{\renewcommand\iven{\nonscript\,\delimsize\vert\nonscript\,} #1}

\begin{document}

\newenvironment{Myitemize}{%
\renewcommand{\labelitemi}{{}}%
\begin{itemize}[nosep]}{\end{itemize}}

\maketitle

\newcommand{\myitem}{\stepcounter{enumi}\item[(\theenumi)]}%for enumerate with no. in brackets
\newcommand\litem[1]{\item{\bfseries {#1}}}

\thispagestyle{fancy}

\begin{mydef} 
If the random vector $(X,Y)$ has joint \textbf{pdf} $f(x,y)$ with conditional \textbf{pdf} $g_{2}(y|x)$, and if $Z=h(X,Y)$ is a (single-valued) function of (X,Y). Then the conditional expectation of the random variable $Z$, given $X=x$ is 
\begin{equation}
E(Z|x)=\int_{-\infty}^{\infty}{h(x,y)g_{2}(y|x)dy}
\label{eq:}
\end{equation}
\end{mydef} 

\begin{mycases}
(a,b,c are constants; ($X^{*}=X-E(X); Y^{*}=Y-E(Y)$)\\
\begin{flalign}\label{cas}
    & Z=a+bX+cY & \Rightarrow\quad & \!\begin{aligned}[t]\EV{Z \given x}&=\EV{a \given x}+b.\EV{X \given x}+c.\EV{Y \given x} \\&= a+bx+c.\EV{Y \given x} \end{aligned} &\hphantom{Z=a+bX+cY\quad(2)} & \\
   & Z=XY & \Rightarrow\quad & \EV{Z \given x} = x\EV{Y \given x}\\
 & Z = Y & \Rightarrow\quad & \EV{Z \given x} = \EV{Y \given x} = \mu_{Y|x} = \text{The CE of Y given X}\\
 & Z=(Y-\mu_{Y|X})^{2} &\Rightarrow\quad & \EV{Z \given x} = \V{Y \iven x} = \sigma^{2}_{Y|x}=\text{The CV of Y given X}
\rlap{\smash{\raisebox{-10pt}{$\left.\rule{0pt}{17pt}\right\}\quad
\def\stackalignment{r}
\stackanchor{\EV{(Y-\mu_{Y|X})^{2} \given X}\leq\quad}{\EV{Y-\mu_{Y})^{2} \given X}}$}}}\\
 & Z=(Y-\mu_{Y})^{2} & \Rightarrow\quad & \EV{Z \given x} = \V{Y \iven x} + (\mu_{Y|x}-\mu_{Y})^2
\end{flalign}

\end{mycases}

\end{document}

在此处输入图片描述

答案2

使用\mathrlap（来自mathtools），您可以实现您想要的。这不是一个可取的做法，但在某些情况下也许是可以接受的。可以放置\Rightarrow更靠左的位置，在对齐的第三列中插入相关的水平空格（有待通过实验确定）。

以下是详细信息：

\documentclass[leqno,10pt]{article}
\usepackage[utf8]{inputenc}
\usepackage{soulutf8}
\usepackage[margin=0.75in]{geometry}
\def\changemargin#1#2{\list{}{\rightmargin#2\leftmargin#1}\item[]}
\let\endchangemargin=\endlist
\usepackage{fancyhdr}
\pagestyle{fancy}
\lhead{Lecture 1}
\rhead{Handout 3}
\usepackage{mathtools}
\usepackage{enumitem,array}
\usepackage{relsize}
\usepackage{amsmath}
\usepackage{amsthm} %for proof
\newtheorem*{mythm}{Theorem}
\theoremstyle{definition}
\newtheorem*{mydef}{Definition}
\newtheorem*{mycases}{Special Cases}
\title{\ul{Conditional Expectations in Bivariate Probability Distribution}}
\date{}

    \providecommand\given{}
    \DeclarePairedDelimiterXPP\EV[1]{E}(){}{
    \renewcommand\given{\nonscript\,\delimsize\vert\nonscript\,}
    #1}

    \DeclarePairedDelimiterXPP\V[1]{V}(){}{
    \renewcommand\given{\nonscript\,\delimsize\vert\nonscript\,}
    #1}

\begin{document}

\newenvironment{Myitemize}{%
\renewcommand{\labelitemi}{{}}%
\begin{itemize}[nosep]}{\end{itemize}}

\maketitle

\newcommand{\myitem}{\stepcounter{enumi}\item[(\theenumi)]}%for enumerate with no. in brackets
\newcommand\litem[1]{\item{\bfseries {#1}}}

\thispagestyle{fancy}

\begin{mydef}
If the random vector $(X,Y)$ has joint \textbf{pdf} $f(x,y)$ with conditional \textbf{pdf} $g_{2}(y\,\vert\,x)$, and if $Z=h(X,Y)$ is a (single-valued) function of (X,Y). Then the conditional expectation of the random variable $Z$, given $X=x$ is
\begin{equation}
\EV{Z \given x}=\int_{-\infty}^{\infty}{h(x,y)g_{2}(y\,\vert\, x)dy}
\label{eq:}
\end{equation}
\end{mydef}

\begin{mycases}
(a,b,c are constants; ($X^{*}=X-E(X); Y^{*}=Y-E(Y)$)\\
\begin{flalign}\label{cas}
    & Z=a+bX+cY & \Rightarrow\quad &\EV{Z \given x}\!\begin{aligned}[t] &= \EV{a \given x}+b.\EV{X \given x}+c.\EV{Y \given x} \\&= a+bx+c.\EV{Y \given x} \end{aligned} & \hskip 5.1cm &
    \\
  & Z=XY & \Rightarrow \quad & \EV{Z \given x} = x\EV{Y \given x} & & \\
 & Z = Y & \Rightarrow\quad& \EV{Z \given x} = \EV{Y \given x} = \mu_{Y|x} = \text{The CE of Y given X}\\
 & Z=(Y-\mu_{Y|X})^{2} &\Rightarrow\quad & \mathrlap{\begin{rcases}\EV{Z \given x} = \V{Y \given x} = \sigma^{2}_{Y|x}=\text{The CV of Y given X}
\end{rcases}\EV{(Y-\mu_{Y|X})^{2} \given X}\leq\EV{()Y-\mu_{Y})^{2} \given X}}&
\\
 & Z=(Y-\mu_{Y})^{2} & \Rightarrow\quad & \EV{Z \given x} = \V{Y \given x} + (\mu_{Y|x}-\mu_{Y})^2
\end{flalign}
\end{mycases}

\end{document}

在此处输入图片描述

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