\begin{definition}[Definition:Random Variable/Discrete/Definition 2]
Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space. 
Let $\struct {S, \Sigma'}$ be a measurable space. 
Let $X$ be a random variable on $\struct {\Omega, \Sigma, \Pr}$ taking values in $\struct {S, \Sigma'}$. 
Then we say that $X$ is a '''discrete random variable''' on $\struct {\Omega, \Sigma, \Pr}$ taking values in $\struct {S, \Sigma'}$ {{iff}}:
:the image of $X$ is a countable subset of $\Omega'$.
Category:Definitions/Random Variables
\end{definition}