Let $Z_0, Z_1, \ldots, Z_N$ be the Radon-Nikod´ym derivative process on the coin flip space $\Omega = \big\{\omega=\omega_1\ldots\omega_N: \omega_j \in\{ H,T \} \big\}$ where $H$ and $T$ stand for Head and Tail respectively.
Prove or disprove that the Radon-Nikod´ym derivative process is a Markov process.