The probabilistic functor $P$ sends a measurable space $X$ to the space of probability measures on $X$ endowed with $\sigma$-algebra generated by evaluation maps, and measurable maps $f:X\to Y$ to pushforwards of measures $f_*:P(X)\to P(Y)$. There are versions of $P$ on Borel/Polish spaces only (in this case $P(X)$ is endowed with the topology of weak convergence) etc.

The notation $P(X)$ is rather natural, but I have often seen it also used for a very similar powerset functor. I wonder which single-letter notation is the most commonly used for the probabilistic functor. Although this question is not of a technical level, it seems to me that MO community may have better suggestions than MSE one, so I post it here.