My book said that a random variable $X(\omega)$ is a function which maps each outcome $\omega$ of the sample space on a real number and the set of the outcomes which verify the inequality:
$$ \left\lbrace X(\omega) \leq a \right\rbrace $$
with $a$ real parameter, have to be an event for all value of $a$.
What does the above inequality mean? Can you explain it with an example please?
Thank you for your willingness.