I'm having trouble with the following statement:
For the stochastic process $(M_t)_{t\in[0,T]}$ to be a martingale it suffices to show that \begin{equation}\label{green} \mathbb{E}[(M_t-M_s)\prod_{i=1}^{n}f_i(M_{s_i})]=0, \end{equation} using a standard monotone class argument, where $f_i$ are continuous, bounded functions on $\mathbb{R}$ and $\{s_1,...,s_n\}\subseteq [0,s]$.
I've already shown that the process is adapted and integrable (it is bounded), but I fail to show the martingale property from the equation above.