Let \(\mu, u\) be \(\sigma\)-finite measures on the measurable space \((X, \mathscr{A})\). Let \(\left(\mathscr{A}_{n}ight)_{n \in \mathbb{N}}\) be a filtration of sub- \(\sigma\)-algebras of \(\mathscr{A}\) such that \(\mathscr{A}=\sigma\left(\bigcup_{n \in \mathbb{N}} \mathscr{A}_{n}ight)\) and then denote \(\mu_{n}:=\left.\muight|_{\mathscr{A}_{n}}\) and \(u_{n}:=\) \(\left.uight|_{\mathscr{A}_{n}}\). If \(\mu_{n} \ll u_{n}\) for all \(n \in \mathbb{N}\), then \(\mu \ll u\). Find an expression for the density \(d \mu / d u\).