Let \(\left(u_{n}ight)_{n \in \mathbb{N}},\left(w_{n}ight)_{n \in \mathbb{N}}\) be two sequences of measurable functions on \((X, \mathscr{A}, \mu)\). Suppose that \(u_{n} \stackrel{\mu}{\longrightarrow} u\) and \(w_{n} \stackrel{\mu}{\longrightarrow} w\). Show that \(a u_{n}+b w_{n}, a, b \in \mathbb{R}, \max \left\{u_{n}, w_{n}ight\}, \min \left\{u_{n}, w_{n}ight\}\) and \(\left|u_{n}ight|\) converge in measure and find their limits.