Radon Nykodym derivative process Let $(\Omega, \mathcal{F}, \mathbb{P})$ be a probability space and a random variable $Z$ satisfying $\mathbb{E}Z=1$. Define the R-N random process $$Z(t)=\mathbb{E}[Z|\mathcal{F(t)}]$$For $0\leq s\leq t \leq T$, $$\mathbb{E}[Z(t)|\mathcal{F(s)}]=\mathbb{E}[\mathbb{E}[Z|\mathcal{F(t)}]|\mathcal{F(s)}]=\mathbb{E}[Z|\mathcal{F(s)}]=Z(s).$$
Can someone explain how the second equality is possible in the above line? Thanks! 

This is a basic property of conditional expectations: if $\mathcal G_1 \subset\mathcal G_2$ then $E(Z|\mathcal G_1)=E(E(Z|\mathcal G_2)|\mathcal G_1)$. You can prove it easily using definition of conditional expectation.
