In Folland's Real analysis, two of properties of measures are stated as follows:
Let $(X,\mathcal{M}, \mu)$ be a measure space.
Continuity from below: If $\{E_j\}_1^{\infty} \subset \mathcal{M}$ and $E_1 \subset E_2 \subset \cdots$, then $\mu(\bigcup_1^{\infty} E_j) = \lim_{j \to \infty} \mu(E_j)$
Similarly,
Continuity from above: If $\{E_j\}_1^{\infty} \subset \mathcal{M}$, $E_1 \supset E_2 \supset \cdots$ and $\mu(E_1) < \infty$. Then $\mu(\bigcap_1^{\infty} E_j) = \lim_{j \to \infty} \mu(E_j)$
I do not understand the point of these statements. How they are related to continuity for example?