Show that [mathscr{P}=left{Gamma: Gamma subset[0, T] times Omega, Gamma cap([0, t] times Omega) in mathscr{B}[0, t] otimes

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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.

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