Definition:Random Variable/Discrete/Definition 2

Definition
Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.

Let $\struct {\Omega', \Sigma'}$ be a measurable space.

Let $X$ be a random variable on $\struct {\Omega, \Sigma, \Pr}$ taking values in $\struct {\Omega', \Sigma'}$.

Then we say that $X$ is a discrete random variable on $\struct {\Omega, \Sigma, \Pr}$ taking values in $\struct {\Omega', \Sigma'}$ :


 * the image of $X$ is a countable subset of $\Omega'$.