Continuity of Measure (Stein Cor. 3.3)

Let $\{E_j\}$ be a sequence of Lebesgue measurable sets of $\mathbb{R}^d$. Then
(i) If $E_j \nearrow E = \cup_{J=1}^\infty $ then $m(E_j) \longrightarrow m(E)$
(ii) If $E_j \searrow E = \cup_{J=1}^\infty $ and $m(E_k) < \infty$ for some $k\in{\mathbb{N}}$ then $m(E_j) \longrightarrow m(E)$