Let $H$ be a previsible process, i.e. $H$ is measurable with respect to $\mathcal{P}$, where $\mathcal{P}=\sigma(E\times(s,t] : E \in \mathcal{F}_s; s,t \in \mathbb{R}_+)$. Need to show that $H_t$ is $\mathcal{F}_{t-}$-measurable for all $t>0$, where $\mathcal{F}_{t-}=\sigma(\mathcal{F}_s:s
I am trying to show $\{H_t \leq r\} \in \mathcal{F}_s$, for all $s>t$, using the fact that $\{H \le r\} \in \mathcal{P}$. Now $\{H_t \le r\} = \{w | (w,t) \in \{H \le r\}\}$ and I am stuck.
Any hints?