Notation confusion - sigma algebra generated by multiple sigma algebras.

36 Views Asked by At

This is a quick one. Let $(\Omega, \mathcal{F}, \mathbb{P})$ be probabilistc space. Let $\mathcal{F_1}, \mathcal{F_2}, \mathcal{F_3}, ...$ be $\sigma$-algebras such that $\mathcal{F_i} \subset \mathcal{F}$ for all $i$. Question: What is ment by notation $\sigma (\mathcal{F}_n, \mathcal{F}_{n+1}, ..) $? Is it the same as $$\sigma (\bigcup_{k=n}^{\infty} \mathcal{F}_k )$$ or maybe $$\sigma(\bigcap_{k=n}^{\infty} \mathcal{F}_k )$$ My textbook omitts the definition, and I can't find it's meaning anywhere online. Forgive me if it's a dumb question.