Definition:Random Variable/Continuous

Definition
Let $$\mathcal E$$ be an experiment with a probability space $$\left({\Omega, \Sigma, \Pr}\right)$$.

A continuous random variable on $$\left({\Omega, \Sigma, \Pr}\right)$$ is a random variable $$X: \Omega \to \R$$ whose cumulative distribution function is continuous for all $$x \in \R$$.