What's a closed countably infinite intersection?

Question

When operating with sigma algebras, what does it mean when we talk about a countably infinite set? And, what are then closed countably infinite interesections?

Answer 1

I expect that you have read that a sigma algebra $\mathcal{A}$ has to be "closed under countably infinite intersections". What this means is that if you have a family $(A_n)$ of elements of $\mathcal{A}$ indexed by the natural numbers $\mathbb{N}$, then the intersection $\bigcap_{n\in\mathbb{N}}A_n$ of all the $A_n$ is also an element of $\mathcal{A}$.