What are notations that have been used for conditional distribution of a random variable $X$ given a $\sigma$-algebra $G$? Is there something analogous to the notations $P[A | G]$, $E[X | G]$, or $E^G[X]$ for conditional probability and conditional expectation?
Or, for that matter, what notations have been used for the distribution (no conditioning) of a random variable $X$? If $X$ is a real random variable, we may use the cumulative distribution function, perhaps written $F_X$; but what if $X$ is not real? -- Gerald A. Edgar email@example.com