How to avoid unbreakable \pmb boxes when typesetting math?

Question

I have a big problem called as a river problem. I'm using the report class defined as:

\documentclass[11pt,notitlepage,a4paper,oneside]{report}
\usepackage[english]{babel}
\usepackage[cp1250]{inputenc}
\usepackage{graphicx,amsmath,amsthm,amssymb,a4wide,eucal,exscale,china2e,varioref,acronym}
\usepackage[left=3.5cm,top=2cm,right=2cm,bottom=2cm]{geometry}
\usepackage{fancyhdr}
\newtheorem{definition}{Definition}[chapter]
\hyphenpenalty=10000
\sloppy
\renewcommand{\chaptermark}[1]{\markboth{#1}{}}
\renewcommand{\chaptermark}[1]{\markright{\thechapter\ #1}}
\renewcommand{\sectionmark}[1]{\markright{\thesection\ #1}}
\fancyhf{} \fancyhead[LO]{\bfseries\nouppercase\rightmark}
\fancyhead[RE]{\bfseries\nouppercase\leftmark}
\fancyhead[RO]{\bfseries\nouppercase\thepage}
\renewcommand{\headrulewidth}{0.5pt}
\renewcommand{\footrulewidth}{0pt}
\setlength{\headsep}{0.2in}
\addtolength{\headheight}{0.5pt}
\fancypagestyle{plain}
{ \fancyhead{}
\renewcommand{\headrulewidth}{0pt}
}

\begin{document}

\begin{definition}
Let $(\Omega,\mathcal{F},\mathsf{F},\mathsf{P})$ be a stochastic
basis. A vector process $\mathbf{W}=(\mathbf{W}_{t},\;t\ge
0)=(W^{1}_{t},W^{2}_{t},\ldots,W^{n}_{t})_{t\ge 0}$ is called an
\pmb{n-dimensional $(\mathcal{F}_{t})$-Wiener process with
covariance matrix $Q$} if it has the following properties:
\begin{itemize}
\item[$\widetilde{(W1)}$] $\mathbf{W}_{t}-\mathbf{W}_{s}$ is
independent of $\mathcal{F}_{s}$ for all $0\le s<t$.
\item[$\widetilde{(W2)}$]
$\mathcal{L}(\mathbf{W}_{t}-\mathbf{W}_{s})=
N(\mathbf{0},(t-s)\mathbf{Q})$ \item[$\widetilde{(W3)}$]
$\mathbf{W}$ has $\mathsf{P}$-a.s. continuous trajectories.
\item[$\widetilde{(W4)}$] $\mathbf{W}_{t}$ is an
$(\mathcal{F}_{t})$-adapted process for every $t\ge 0$.
\end{itemize}
\end{definition}


\end{document}

In some cases the output is really ugly. Is it possible to get rid of "rivers" without deleting the command sloppy, which I need to keep in the document?

Answer 1

Section 8.5 of the Comprehensive LaTeX Symbol List shows various ways to get bold math which seems to be the main problem here. I chose \boldsymbol, microtype is always a good idea and although I prefer paralist over enumitem, the latter is actually needed in this case so I stole egreg's solution for this:

\documentclass[11pt,notitlepage,a4paper,oneside]{report}
\usepackage[english]{babel}
\usepackage[cp1250]{inputenc}
\usepackage{graphicx,amsmath,amsthm,amssymb,a4wide,eucal,exscale,varioref,acronym,china2e}
\usepackage[left=3.5cm,top=2cm,right=2cm,bottom=2cm]{geometry}
\usepackage{fancyhdr}
\usepackage{microtype}
\usepackage{enumitem}
\newtheorem{definition}{Definition}[chapter]
\renewcommand{\chaptermark}[1]{\markboth{#1}{}}
\renewcommand{\chaptermark}[1]{\markright{\thechapter\ #1}}
\renewcommand{\sectionmark}[1]{\markright{\thesection\ #1}}
\fancyhf{} \fancyhead[LO]{\bfseries\nouppercase\rightmark}
\fancyhead[RE]{\bfseries\nouppercase\leftmark}
\fancyhead[RO]{\bfseries\nouppercase\thepage}
\renewcommand{\headrulewidth}{0.5pt}
\renewcommand{\footrulewidth}{0pt}
\setlength{\headsep}{0.2in}
\addtolength{\headheight}{0.5pt}
\fancypagestyle{plain}
{ \fancyhead{}
\renewcommand{\headrulewidth}{0pt}
}

\begin{document}

\begin{definition}
Let $(\Omega,\mathcal{F},\mathsf{F},\mathsf{P})$ be a stochastic
basis. A vector process $\mathbf{W}=(\mathbf{W}_{t},\;t\ge
0)=(W^{1}_{t},W^{2}_{t},\ldots,W^{n}_{t})_{t\ge 0}$ is called an
\textbf{n-dimensional $\boldsymbol{(\mathcal{F}_{t})}$-Wiener process with
covariance matrix $\mathbf{Q}$} if it has the following properties:
\begin{enumerate}[label=$\widetilde{(W\arabic*)}$,leftmargin=*]
\item $\mathbf{W}_{t}-\mathbf{W}_{s}$ is independent of $\mathcal{F}_{s}$ for all $0\le s<t$.
\item $\mathcal{L}(\mathbf{W}_{t}-\mathbf{W}_{s})=N(\mathbf{0},(t-s)\mathbf{Q})$
\item $\mathbf{W}$ has $\mathsf{P}$-a.s. continuous trajectories.
\item $\mathbf{W}_{t}$ is an $(\mathcal{F}_{t})$-adapted process for every $t\ge 0$.
\end{enumerate}
\end{definition}
\end{document}

I hope this is how you want it to look like:

Answer 2

Use the microtype package and if it need be the ragged2e package. It will improve the text tremendously as you will observe by comparing your minimal with the below:

before

after

without "poor man's bold"

However, the bigger source of the problem is you are adding too many inline equations and symbols, that neither add to the readability of your publication nor to the typography of the text.

Additional Explanatory Notes

The macro \pmb stands for poor man's bold. In the early days of TeX many printers were incapable of printing in bold. Knuth in the TeXBook gave an example of "poor man's bold," (The TeXbook, p. 386) which can be typeset obtained by overprinting the normal weight symbol with slight offsets. See https://tex.stackexchange.com/a/8957/963 for a bit of additional explanations. Don't use it rather use \textbf directly.

For most normal texts, it is very difficult and unusual for TeX to produce rivers, provided you do not fiddle with parameters. As the macro \pmb typesets its contents in an box, TeX cannot hyphenate it causing the problems you experienced.

Once you free TeX, from the limitations you imposed on it and you add microtype that will minimize hyphenation the text will improve as you can see in the third image.

Finally, for emphasis is considered better typography to use an italic font.

\documentclass[11pt,notitlepage,a4paper,oneside]{report}
\usepackage[english]{babel}
\usepackage[cp1250]{inputenc}
\usepackage{graphicx,amsmath,amsthm,amssymb,a4wide,eucal,exscale,china2e,varioref,acronym,microtype,ragged2e}
\usepackage[left=3.5cm,top=2cm,right=2cm,bottom=2cm]{geometry}
\usepackage{fancyhdr}
\newtheorem{definition}{Definition}[chapter]
%\hyphenpenalty=10000
%\sloppy
\renewcommand{\chaptermark}[1]{\markboth{#1}{}}
\renewcommand{\chaptermark}[1]{\markright{\thechapter\ #1}}
\renewcommand{\sectionmark}[1]{\markright{\thesection\ #1}}
\fancyhf{} \fancyhead[LO]{\bfseries\nouppercase\rightmark}
\fancyhead[RE]{\bfseries\nouppercase\leftmark}
\fancyhead[RO]{\bfseries\nouppercase\thepage}
\renewcommand{\headrulewidth}{0.5pt}
\renewcommand{\footrulewidth}{0pt}
\setlength{\headsep}{0.2in}
\addtolength{\headheight}{0.5pt}
\fancypagestyle{plain}
{ \fancyhead{}
\renewcommand{\headrulewidth}{0pt}
}

\begin{document}

\begin{definition}
Let $(\Omega,\mathcal{F},\mathsf{F},\mathsf{P})$ be a stochastic
basis. A vector process $\mathbf{W}=(\mathbf{W}_{t},\;t\ge
0)=(W^{1}_{t},W^{2}_{t},\ldots,W^{n}_{t})_{t\ge 0}$ is called an
\pmb{n-dimensional $(\mathcal{F}_{t})$-Wiener process with
covariance matrix $Q$} if it has the following properties:
\begin{itemize}
\item[$\widetilde{(W1)}$] $\mathbf{W}_{t}-\mathbf{W}_{s}$ is
independent of $\mathcal{F}_{s}$ for all $0\le s<t$.
\item[$\widetilde{(W2)}$]
$\mathcal{L}(\mathbf{W}_{t}-\mathbf{W}_{s})=
N(\mathbf{0},(t-s)\mathbf{Q})$ \item[$\widetilde{(W3)}$]
$\mathbf{W}$ has $\mathsf{P}$-a.s. continuous trajectories.
\item[$\widetilde{(W4)}$] $\mathbf{W}_{t}$ is an
$(\mathcal{F}_{t})$-adapted process for every $t\ge 0$.
\end{itemize}
\end{definition}
\end{document}

Answer 3

Here's a way to solve some your river problems: first of all no \sloppy declaration; then the usual way to treat definitions: text in upright type and the defined term in italics.

\documentclass[11pt,notitlepage,a4paper,oneside]{report}
\usepackage[english]{babel}
\usepackage{amsmath,amsthm}
\usepackage[left=3.5cm,top=2cm,right=2cm,bottom=2cm]{geometry}

\usepackage{microtype}
\usepackage{enumitem}
\usepackage{fancyhdr}

\renewcommand{\chaptermark}[1]{\markboth{#1}{}}
\renewcommand{\chaptermark}[1]{\markright{\thechapter\ #1}}
\renewcommand{\sectionmark}[1]{\markright{\thesection\ #1}}
\fancyhf{} 
\fancyhead[LO]{\bfseries\nouppercase\rightmark}
%\fancyhead[RE]{\bfseries\nouppercase\leftmark}
\fancyhead[RO]{\bfseries\nouppercase\thepage}
\renewcommand{\headrulewidth}{0.5pt}
\renewcommand{\footrulewidth}{0pt}
\setlength{\headsep}{0.2in}
\addtolength{\headheight}{0.5pt}
\fancypagestyle{plain}
{ \fancyhead{}
\renewcommand{\headrulewidth}{0pt}
}

%%% Theorem-like environments %%%
\theoremstyle{definition}
\newtheorem{definition}{Definition}[chapter]

\theoremstyle{plain}
\newtheorem{proposition}[definition]{Proposition}
\newtheorem{theorem}[definition]{Theorem}
\newtheorem{lemma}[definition]{Lemma}
\newtheorem{corollary}[definition]{Corollary}

\theoremstyle{remark}
\newtheorem{example}[definition]{Example}
\newtheorem{remark}[definition]{Remark}
\newtheorem{notation}[definition]{Notation}
\newtheorem{convention}[definition]{Convention}

\begin{document}

\chapter{Wiener processes}

\begin{definition}
Let $(\Omega,\mathcal{F},\mathsf{F},\mathsf{P})$ be a stochastic
basis. A vector process $\mathbf{W}={(\mathbf{W}_{t},\,t\ge 0)}=
(W^{1}_{t},W^{2}_{t},\ldots,W^{n}_{t})_{t\ge 0}$ is called an
\emph{$n$-dimensional $(\mathcal{F}_{t})$-Wiener process with
covariance matrix~$Q$} if it has the following properties:
\begin{enumerate}[label=$\widetilde{(W\arabic*)}$,leftmargin=*]
\item $\mathbf{W}_{t}-\mathbf{W}_{s}$ is independent of $\mathcal{F}_{s}$
  for all $0\le s<t$;

\item $\mathcal{L}(\mathbf{W}_{t}-\mathbf{W}_{s})=N(\mathbf{0},(t-s)\mathbf{Q})$;

\item $\mathbf{W}$ has $\mathsf{P}$-a.s.\ continuous trajectories;

\item $\mathbf{W}_{t}$ is an $(\mathcal{F}_{t})$-adapted process for every $t\ge 0$.
\end{enumerate}
\end{definition}

\end{document}

Notice how \emph is used for the defined term; the definition environment is declared after \theoremstyle{definition}, which causes all subsequent theorem-like environments to have the body text in upright type.

The enumerated list is best treated with enumitem features.

I've removed all packages not essential for the example.

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