# Definition:Disjoint Union (Probability Theory)

## Definition

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.

## Sources

- 2005: René L. Schilling:
*Measures, Integrals and Martingales*... (previous) ... (next): $\S 2$