A deterministic <càdlàg function> is <Borel measurable function>[Borel measurable]. The sets $\Omega\times(s,t]$ and $\Omega\times\{0\}$ show that $\mathcal B([0,\infty))$ is contained in $\mathcal P$. Therefore every deterministic càdlàg function, regarded as a process constant in $\omega$, is predictable.

Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 202 / 2 / e / Solution

 Solution (source code)