Past exam of the martingales and financial mathematics course of the University of Oxford / 2008 / A / 1 / b / iii

If $S\le T$, then $\{S\le T\}=\Omega$. The previous result says that every $A\in {\mathcal{F}}_S$ equals $A\cap \{S\le T\}\in {\mathcal{F}}_T$. ThusInformation known at the earlier stopping time remains known at the later stopping time.