Let $(\Omega, \mathscr{F})$ be a measurable space. Let $\mathscr{P}$ be the space of all valid probability measures on this space. Clearly, $\mathscr{P} \subset [0,1]^\mathscr{F}$. I was wondering if there exists a standard notation for $\mathscr{P}$, i.e., using $\mathscr{F} $ and/or $\Omega$.
Please note that Space of probability measures "complete"? (In the other sense) does not answer my question.