In David Williams's Probability with Martingales, there is a remark regarding conditional expectation of a random variable conditional on a $\sigma$-algebra:
The 'a.s.' ambiguity in the definition of conditional expectation is something one has to live with in general, but it is sometimes possible to choose a canonical version of $E(X| \mathcal{Q})$.
What is "canonical version of $E(X| \mathcal{Q})$", and what are some cases when it is possible to choose it?
I don't want to be misleading, but is it referring to elementary definitions of conditional distribution and conditional expectation when they exist i.e. when the denominators are not zero?
Thanks and regards!