Kolmogorov

In the measure-theoretic formalization of probability theory, a random variable is defined as a measurable function X from a probability space \scriptstyle (\Omega, \mathcal{F}, \operatorname{P}) to measurable space \scriptstyle (\mathcal{X},\mathcal{A}). A probability distribution is the pushforward measure X*P = PX −1 on \scriptstyle (\mathcal{X},\mathcal{A}).

http://en.wikipedia.org/wiki/Probability_distribution#Kolmogorov_definition