Definition

Recall the (R) Set of Predictable Rectangles, $\mathcal{R}$. We denote by $\mathcal{A}$ the ring generated by $\mathcal{R}$, i.e. the closure under finite union and proper complement.

Note

Any element of $\mathcal{A}$ can be written as the union of finitely many disjoint elements of $\mathcal{R}$ i.e. $\forall (A_{n})_{n\in\mathbb{N}}\subset \mathcal{R}$ s.t. $A_{i}\cap A_{j}=\emptyset \ \forall i\not=j$ then $\exists B\in\mathcal{A}$ s.t. $$B=\bigcup_{n\in\mathbb{N}}A_{n}$$