Let $X_t$ a continuous stochastic process. My question is: How many probability measures $\mathbb{P}$ there exist that make $X$ a martingale? Is there any theorem to find them? my question is because I am not sure if there exist two measures $\mathbb{P}$ and $\mathbb{Q}$ for wich $\mathbb{E}^\mathbb{P}[X_t|\mathcal{F_s}]=X_s$ and $\mathbb{E}^\mathbb{Q}[X_t|\mathcal{F_s}]=X_s$ my guess is that it is true by Radom-Nykodim, but is there a way to find all of these measures?
Any help or advice is welcome, thank you very much!.