Probability Terminology – MathOverflow

This is strictly a low-level terminology question. If I have a probability space $Omega$ and a measurable space $S$, then a random variable $X:Omegarightarrow S$ gives rise via pushforward to a probability distribution on $S$. I want to assume that that every probability distribution on $S$ arises in this way. Is there a name for that condition or do I need to make one up?