An Introduction to Probability and Statistical Inference, 2nd Edition

For the formulation of the next result, the concept of a partition of $\mathcal{S}$ is required. The events {A₁, A₂, …, A_n} form a partition of $\mathcal{S}$, if these events are pairwise disjoint, A_i ∩ A_j = Ø, i ≠ j, and their union is $\mathcal{S}$, ${\displaystyle {\cup }_{j=1}^n{A}_j=\mathcal{S}}$. Then it is obvious that any event B in $\mathcal{S}$ may be expressed as follows, in terms of a partition of $\mathcal{S}$; namely, $B={\displaystyle {\cup }_{j=1}^n(A_j\cap B)}$