Reference request: dimension of convex hull of n random points

Question

Let $X$ be an i.i.d. random sample of $n$ points in $\mathbb{R}^d$ from a probability distribution that is absolutely continuous with respect to the $d$-dimensional Lebesgue measure. Assume $n>d$. I am looking for a textbook reference that shows that the dimension of the convex hull of $X$ is $d$ with probability 1.