Definition

We denote by $\mathscr{P}$ the σ-algebra on $\mathbb{R}^{+}\times\Omega$ generated by the predictable rectangles, $\mathcal{R}$ i.e. generated by sets of the form$$\begin{align*} &\{ 0 \}\times F_{0},&F_{0}\in\mathcal{F}_{0}\\ &(s,t]\times F, &\forall0\le s<t,F\in\mathcal{F} \end{align*}$$

Note

We have that $$\mathcal{R}\subset \mathcal{A}\subset \mathscr{P}$$