Predictable representation in a Rademacher filtration
= Predictable representation in a Rademacher filtration
If $\mathcal F_n$ is generated by independent symmetric signs $\xi_1,\ldots,\xi_n$, every martingale has predictable coefficients $B_n$ such that
$$
M_n=M_0+\sum_{k=1}^nB_k\xi_k.
$$
One may take $B_n=\mathbb E[M_n\xi_n\mid\mathcal F_{n-1}]$.