Show that a measure space \((X, \mathscr{A}, \mu)\) is \(\sigma\)-finite if, and only if, there exists a sequence of measurable sets \(\left(E_{n}ight)_{n \in \mathbb{N}} \subset \mathscr{A}\) such that \(\bigcup_{n \in \mathbb{N}} E_{n}=X\) and \(\mu\left(E_{n}ight)<\infty\) for all \(n \in \mathbb{N}\).