Let \(\mu^{*}\) be an outer measure on \(X\), and let \(A_{1}, A_{2}, \ldots\) be a sequence of mutually disjoint \(\mu^{*}\)-measurable sets, i.e. \(A_{i} \in \mathcal{A}^{*}, i \in \mathbb{N}\). Show that

\[\mu^{*}\left(Q \cap \bigcup_{i} A_{i}ight)=\sum_{i=1}^{\infty} \mu^{*}\left(Q \cap A_{i}ight) \quad \text { for all } Q \subset X\]