Two conditional equations in the same line

Question

I want to define two functions conditionally as in How to write conditional equations with one-sided curly brackets, but I want to write the two equations on the same line. Is there a way for this?

Answer 1

No further special constructs are needed for this, just add some space after the first definition with e.g. \qquad:

\documentclass{article}

\usepackage{mathtools}

\begin{document}

\begin{equation*}
  w_{n}(x) =
  \begin{dcases*}
    \frac{1}{2^{n+1}(1+\mu(E_{n}))},&if \( x\in E_{n}\),\\
    0,&otherwise,
  \end{dcases*}
  \qquad
  u_{n}(x) =
  \begin{dcases*}
    \frac{\mu(E_{n})}{2^{n+1}(1+\mu(E_{n}))},&if \( x\in E_{n}\),\\
    0,&otherwise.
  \end{dcases*}
\end{equation*}

\end{document}

If a \qquad is too much, you can reduce to a \quad. It is best to make the punctuation part of the cases statements, rather than putting it outside these blocks.