# How do I break a long equation?

I have a long equation that it was hard for me to break so that it appears professional. How can I do it?

$$\begin{split} &\mathbb{P}\left( \left. Z_{1}\in dx_{1},Z_{2}\in dx_{2},\cdots ,Z_{n}\in dx_{n}\right\vert Z_{n+1}=x_{n+1}\right) \\ \qquad &=f_{Z_{n+1}}\left(x_{n+1}\right) ^{-1}\left[ \mathbb{P}\left( \left\{ Z_{1}\in dx_{1},Z_{2}\in dx_{2},\cdots ,Z_{n}\in dx_{n}\right\} \cap \left\{ Z_{n+1}=x_{n+1}\right\} \right) \right] \\ =f_{Z_{n+1}}\left( x_{n+1}\right) ^{-1}\times \mathbb{\pi } \\ =e^{-x_{n+1}}dx_{1}\cdots dx_{n+1}/f_{Z_{n+1}}\left( x_{n+1}\right) \\ =n!x^{-n}dx_{1}\cdots dx_{n} \end{split}$$


You're not far. Remove all \left and \right tokens that only do bad, in this context; there's just a pair of brackets that asks for being a bit larger (with \bigl and \bigr).

Also some help is needed for the dots in the final two lines; use \mid instead of \vert, for better spacing and don't forget \, after the factorial.

Last thing: I added empty superscripts to f_{Z_{n+1}}, so the subscript is slightly moved down.

\documentclass{article}
\usepackage{mathtools}
\usepackage{amsfonts} % for \mathbb

\DeclareMathOperator{\PR}{\mathbb{P}}

\begin{document}
$$\begin{split} &\PR(Z_{1}\in dx_{1},Z_{2}\in dx_{2},\dots ,Z_{n}\in dx_{n}\mid Z_{n+1}=x_{n+1}) \\ &\quad =f^{}_{Z_{n+1}}(x_{n+1}) ^{-1}\bigl[ \PR( \{ Z_{1}\in dx_{1},Z_{2}\in dx_{2},\dots,Z_{n}\in dx_{n}\} \\ &\qquad\qquad \cap\{Z_{n+1}=x_{n+1}\})\bigr] \\ &\quad =f^{}_{Z_{n+1}}( x_{n+1}) ^{-1}\times \pi \\ &\quad =e^{-x_{n+1}}dx_{1}\dotsm dx_{n+1}/f^{}_{Z_{n+1}}(x_{n+1}) \\ &\quad =n!\,x^{-n}dx_{1}\dotsm dx_{n} \end{split}$$
\end{document}


• why not an outer multline with all lines but the first either split or aligned? – barbara beeton Mar 18 '16 at 14:33
• @barbarabeeton I prefer the equals signs to be near the left side, like if the first line were X&=\PR(...) – egreg Mar 18 '16 at 14:35

Some suggestions:

• Keep using a split environment, but provide alignment points on all lines

• Use an aligned environment to the right of the = symbol in row 2 to break up that line into two separate lines

• Don't overuse \left and \right; in fact, for the equations at hand, they're not needed at all.

• Don't use \cdots for the equations at hand. Instead, use \dots in the first two rows and \dotsm ("multiplicate dots") in the final two rows.

• There is no "Blackboard Bold" version of \pi; hence, \mathbb{\pi } is the same as \pi. If you must produce a bold version of the symbol, write \boldsymbol{\pi}; alternatively, load the bm package and write \bm{\pi}.

\documentclass{article}
\usepackage{amsmath,amsfonts,bm}

\begin{document}
\begin{split} \mathbb{P}( &Z_{1}\in dx_{1},Z_{2}\in dx_{2},\dots, Z_{n}\in dx_{n} \mid Z_{n+1}=x_{n+1}) \\ &=\!\begin{aligned}[t] f_{Z_{n+1}}^{} (x_{n+1})^{-1} \bigl[ \mathbb{P}(\{ &Z_{1}\in dx_{1}, Z_{2}\in dx_{2}, \dots , Z_{n}\in dx_{n}\} \\ &\cap \{ Z_{n+1}=x_{n+1}\} ) \bigr] \end{aligned}\\ &=f_{Z_{n+1}}( x_{n+1})^{-1} \times \bm{\pi} \\ &=e^{-x_{n+1}}\,dx_{1}\dotsm dx_{n+1} / f_{Z_{n+1}}( x_{n+1}) \\ &=n!\,x^{-n}\,dx_{1}\dotsm dx_{n} \end{split}
\end{document}


I propose a solution with multline and aligned. The geometry package yields more sensible margins, if you don't use margin notes. Finally, I simplified your code, using the \DeclarePairedDelimiter commad form mathtools: I defined a \Prob+\given command for conditional probabilities, and a \set command, which have variable-sized delimiters if used in their starred version, or with an option (\big, \Big, &c.):

\documentclass{article}
\usepackage{mathtools,amsfonts} % for 'dcases' environment
\usepackage{xparse} \usepackage[showframe]{geometry}

\DeclarePairedDelimiterXPP\Prob[1]{\mathbb P}(){}{
\newcommand\given{\nonscript\:\delimsize\vert\nonscript\:}
#1}

\DeclarePairedDelimiterX{\set}[1]\{\}{\setargs{#1}}
\NewDocumentCommand{\setargs}{>{\SplitArgument{1}{;}}m} {\setargsaux#1}
\NewDocumentCommand{\setargsaux}{mm}
{\IfNoValueTF{#2}{\nonscript\,#1\nonscript\,}{\nonscript\,#1\nonscript\;{;}
\nonscript\:\allowbreak #2\nonscript\,}}

\begin{document}

\begin{multline}
\Prob{ Z_{1} \in dx_{1},Z_{2} \in dx_{2}, \dots ,Z_{n}\in
dx_{n}\given Z_{n+1} =x_{n+1}} \\
\begin{aligned}
& =f_{Z_{n+1}}\left(x_{n+1}\right) ^{-1}\left[ \Prob*{\set*{ Z_{1} \in dx_{1},Z_{2} ∈
dx_{2}, \dots ,Z_{n} \in dx_{n}} \cap \set*{ Z_{n+1}=x_{n+1}}} \right] \\
& =f_{Z_{n+1}}\left( x_{n+1}\right) ^{-1} \times \mathbb{\pi } \\
& =e^{-x_{n+1}}dx_{1}\dotsm dx_{n+1}/f_{Z_{n+1}}\left( x_{n+1}\right) \\
& =n!\,x^{-n}dx_{1} \dotsm dx_{n}
\end{aligned}
\end{multline}

\end{document}


• I don't think it's typographically appropriate to use \cdots in comma-delimited lists -- see rows 1 and 2. Consider using either \dots or \dotsc ("dots between commas"). Also, \mathbb{\pi} is suspect. – Mico Mar 18 '16 at 15:12
• @Mico: I just took the code from the O.P and didn't notice. But you're righht, I'll update my answer. Thanks for pointing it – Bernard Mar 18 '16 at 15:21