----
> [!theorem] Theorem. ([[Dynkin's Ο-π theorem]])
> If $\mathcal{P}$ is a [[Ο-system]] and $\mathcal{D}$ is a [[Dynkin system|π-system]] such that $\mathcal{P} \subset \mathcal{D}$, [[Ο-algebra generated by a set collection|then]] $\sigma(\mathcal{P}) \subset \mathcal{D}$.
^theorem
> [!note] Remark.
![[class methods in measure theory#^the-property-playbook]]
> [!proof]- Proof. ([[Dynkin's Ο-π theorem]])
> Omitted in our course.
----
####
-----
#### References
> [!backlink]
> ```dataview
> TABLE rows.file.link as "Further Reading"
> FROM [[]]
> FLATTEN file.tags as Tag
> WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom"
> GROUP BY Tag
> ```
> [!frontlink]
> ```dataview
> TABLE rows.file.link as "Further Reading"
> FROM outgoing([[]])
> FLATTEN file.tags as Tag
> WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom"
> GROUP BY Tag
> ```