Take the tour ×  On page 217 of the book Probability Essentials
By Jean Jacob and Philip Protter found an issue that can not do,
is about martingales and stopping times. If anyone has any tips
on how to do, I'd appreciate it a lot:  $$E \{ E (Y\mid F_T)\mid
F_S\} = E \{ E (Y\mid F_S)\mid F_T\} = E (Y\mid F_{T \wedge
S})$$  $T$, $S$ are stopping times.  share|improve this question
What did you try? –  Did Sep 14 '12 at 18:13 tips: with $Y_T =
\mathbb E(Y | F_T)$ etc. $Y_{T\wedge S},Y_T$ is martingale. Also
$\lbrace T < S \rbrace \in F_S$ and of course $F_T$ –  mike Sep
15 '12 at 10:35 add comment  1 Answer  I have a method but it
assumes T and S are bounded stopping times. So let T and S be
bounded stopping times. In Jacod and Protter, the theory is for
Discrete time martingales and so T and S take on non negative
integer values. (Note: All random variable equalities and
inequalities are almost sure ones).  Let $M_t = E[Y|F_t]$  Then
we need to show $$ E[M_T|F_S] = M_{S\wedge T}$$  Let $$A=
\{\omega : S(w) \le