\begin{definition}[Definition:Disjoint Union (Probability Theory)]
Let $\CC$ be a collection of pairwise disjoint sets.
That is, for all sets $A, B \in \CC: A \ne B \implies A \cap B = \O$.
Then the union of all sets in $\CC$ is called their '''disjoint union''':
:$\ds \bigsqcup_{A \mathop \in \CC} A \equiv \bigcup_{A \mathop \in \CC} A$
That is, in this context the term '''disjoint union''' means '''union of sets which are pairwise disjoint'''.
\end{definition}