Show that \[\mathscr{P}=\left\{\Gamma: \Gamma \subset[0, T] \times \Omega, \Gamma \cap([0, t] \times \Omega) \in \mathscr{B}[0, t] \otimes \mathscr{F}_{t} \quad \text { for all } t \leqslant Tight\}\] is a \(\sigma\)-algebra.