Definition:Disjoint Union (Probability Theory)

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Let $\mathcal C$ be a collection of pairwise disjoint sets.

That is, for all sets $A, B \in \mathcal C: A \ne B \implies A \cap B = \varnothing$.

Then the union of all sets in $\mathcal C$ is called their disjoint union:

$\displaystyle \bigsqcup_{A \mathop \in \mathcal C} A \equiv \bigcup_{A \mathop \in \mathcal C} A$

That is, in this context the term disjoint union means union of sets which are pairwise disjoint.

Also see

Compare the more sophisticated definition for the disjoint union in the context of set theory.