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Answer by Rhys Steele for The closure of the elementary processes are the...

First, it is important to notice that (not unusually) Roger and Williams have, at the point you are looking at, restricted their integrator $M$ to be a continuous $L^2$-bounded martingale. This means...

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The closure of the elementary processes are the predictable processes

I am reading "Diffusion, Markov Processes and Martingales" by Roger/Williams, which state the following version of the monotone class theorem applied to bounded elementary processes...

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