I have been going through some research papers related to information theory. Very often, I have come across this concept of independent versions and conditionally independent versions of a given random variable. I have some difficulty understanding this concept.
More precisely, say for a random variable $X$ and some measurable function $F$, $Z=F\left(X\right)$ be another random variable. What does it exactly mean when they say: "Let $X$ and $X'$ be two conditionally independent versions of $X$ given $Z$" ?
Though I understand what the above statement mathematically means, can anyone give me a more meaningful and intuitive interpretation of the above statement. Also I have the following doubt. How can we be sure that there exists such a version ?