# bracket on right side to the following identities and give it numbering as (*)

I want bracket on right side to the following identities and give it numbering as (*)

\begin{align*}
\mu(E)&=\sup\{\mu(K)~:~ K \text{ is a compact subset of } E \}\\
&=\inf\{\mu(U)~:~ U \text{ is an open set containing } E \}
\end{align*}


I tried to do it as

\left \begin{align*}
\mu(E)&=\sup\{\mu(K)~:~ K \text{ is a compact subset of } E \}\\
&=\inf\{\mu(U)~:~ U \text{ is an open set containing } E \}
\end{align*}\right\}


Maybe something like the following, which uses an rcases environment (provided by the mathtools package):
\documentclass{article}
$$\mu(E)= \begin{rcases} \sup\{\mu(K)\} \colon \text{K is a compact subset of E}\\ \inf\{\mu(U)\} \colon \text{U is an open set containing E} \end{rcases} \tag{*}$$