\begin{definition}[Definition:Dynkin System Generated by Collection of Subsets]
Let $X$ be a set.
Let $\GG \subseteq \powerset X$ be a collection of subsets of $X$.
Then the '''Dynkin system generated by $\GG$''', denoted $\map \delta \GG$, is the smallest Dynkin system on $X$ that contains $\GG$.
That is, $\map \delta \GG$ is subject to:
:$(1):\quad \GG \subseteq \map \delta \GG$
:$(2):\quad \GG \subseteq \DD \implies \map \delta \GG \subseteq \DD$ for any Dynkin system $\DD$ on $X$
In fact, $\map \delta \GG$ always exists, and is unique, as proved on Existence and Uniqueness of Dynkin System Generated by Collection of Subsets.
\end{definition}