Vertical Line and \split

Question

\documentclass[a4paper,12pt]{article}   
\usepackage{mathtools}

\begin{document}
\begin{equation}
    \mathcal{A}(x) \coloneqq \left\{
    \pi(t) \text{ prog. mbl. } \bigg \vert \: \begin{split}
        & E(U(X^{\pi,x}(T))^-) < \infty, X^{\pi,x}(T) \geq B \text{ a.s.}, \\
        & \int_0^{T} \Vert \pi(t)X^{\pi,x}(t)\Vert^2 dt < \infty a.s.
    \end{split}  \right\}
\end{equation}

\end{document}

produces

Is there a way to adapt the vertical line s.t. it spans across both lines, separated by \split? Thanks.

Answer 1

You want to use \middle and aligned:

\documentclass[a4paper,12pt]{article}   
\usepackage{mathtools}

\begin{document}
\begin{equation}
\mathcal{A}(x) \coloneqq 
\left\{
    \pi(t) \text{ prog. mbl.} 
\;\middle\vert\;
\begin{aligned}
  & E(U(X^{\pi,x}(T))^-) < \infty, X^{\pi,x}(T) \geq B \text{ a.s.}, \\
  & \int_0^{T} \lVert \pi(t)X^{\pi,x}(t)\rVert^2 \,dt < \infty \text{ a.s.}
\end{aligned}
\right\}
\end{equation}

\end{document}

Note \lVert and \rVert rather the unqualified \Vert. The correct spacing for relations is \;.

In this particular case, you can fool TeX into thinking that the equation number fits, see https://tex.stackexchange.com/a/348745/4427

\documentclass[a4paper,12pt]{article}   
\usepackage{mathtools,showframe}

\begin{document}
\begin{equation}
\mathcal{A}(x) \coloneqq 
\left\{
    \pi(t) \text{ prog. mbl.} 
\;\middle\vert\;
\begin{aligned}
  & E(U(X^{\pi,x}(T))^-) < \infty, X^{\pi,x}(T) \geq B \text{ a.s.}, \\
  & \int_0^{T} \lVert \pi(t)X^{\pi,x}(t)\rVert^2 \,dt < \infty \text{ a.s.}
\end{aligned}
\right\}
\hspace{10000pt minus 1fil}
\end{equation}

\end{document}

I added showframe just to see that the equation still fits in the margins.

Answer 2

with use of the array environment:

\documentclass[a4paper,12pt]{article}
\usepackage{mathtools}
\DeclarePairedDelimiter\norm{\lVert}{\rVert}

\begin{document}
\begin{equation}
    \mathcal{A}(x) \coloneqq \left\{
    \pi(t) \text{ prog. mbl.} \;
    \begin{array}{| l @{}}
    E(U(X^{\pi,x}(T))^-) < \infty,\, X^{\pi,x}(T) \geq B \text{ a.s.}, \\
    \int\limits_0^{T} \norm*{\pi(t)X^{\pi,x(t)}}^2 dt  < \infty  \text{ a.s.}.
    \end{array}  \right\}
\end{equation}
\end{document}