Past exam of the martingales and financial mathematics course of the University of Oxford / 2008 / A / 3 / a / iii / Solution

A martingale is an adapted process $X_n$ with $\mathbb{E}|X_n|<\infty$ for every $n$ andAdaptedness means that $X_n$ is ${\mathcal{F}}_n$-measurable. Iterating the tower property gives the analogous identity for any two deterministic times $m\le n$.