• $A_i \in \mathcal{F}, \overline{A_i} \in \mathcal{F}$
• $\bigcap_{i=1}^{\infty}A_i \in \mathcal{F}$
• $\bigcup_{i=1}^{n}A_i \in \mathcal{F}$
• $\bigcap_{i=1}^{n}A_i \in \mathcal{F}$
• Let $A_n \in \mathcal{F}$ , Proof :

$\lim_{n \to \infty} P(A_n) = \begin{cases} P(\bigcup_{i=1}^{\infty}A_n), A_1 \subset A_2 \subset A_3 \subset ... \\ P(\bigcap_{i=1}^{\infty}A_n), A1 \supset A_2 \supset A_3 \supset ... \end{cases}$