What would you like to understand?

A sigma-algebra is closed under countable intersections because any countable intersection can be rewritten in terms of complements and countable unions using De Morgan's law. Since a sigma-algebra is already closed under complements and countable unions, it must also be closed under countable intersections.

Conditions: Each $A_k \in \mathcal{F}$.; $\mathcal{F}$ is closed under complements and countable unions.

A sigma-algebra is closed under countable intersections because any countable intersection can be rewritten in terms of complements and countable unions using De Morgan's law. Since a sigma-algebra is already closed under complements and countable unions, it must also be closed under countable intersections.

Conditions: Each $A_k \in \mathcal{F}$.; $\mathcal{F}$ is closed under complements and countable unions.