Theorem

Dynkin

1. If $\mathcal{P}$ is a $\pi$-system and $\mathcal{L}$ is a $\lambda$-system such that $\mathcal{P} \subset \mathcal{L}$ then $\sigma(\mathcal{P}) \subset \mathcal{L}$.
2. If $\mathcal{P}$ is a $\pi$-system then $\sigma(\mathcal{P}) = \mathcal{L}(\mathcal{P})$.