xbeta
Random variable

Let $(\Omega ,ℱ,P)$ be a probability space? and $(Y,\Sigma )$ be a measurable space?. A random variable on $\Omega$ is a measurable function? $X:\Omega \to Y$. Here, $Y$ is called the state space of $X$ (Doob, 1996).

References

Doob, J. L. (1996). The Development of Rigor in Mathematical Probability (1900-1950). American Mathematical Monthly 103, 586–595.