 Notice that the set \(\Delta(E)\) of all probability weights on \(E\) is convex, in that, given any sequence \(\omega_1,\omega_2,\ldots\) of probability weights and any sequence \(t_1,t_2,\ldots\) of non-negative real numbers summing to one, the convex sum or “mixture” \(t_1\omega_1 + t_2\omega_2 +\ldots\) (taken pointwise on \(E)\) is again a probability weight. The extreme points of this convex set are exactly the “point-masses” \(\delta(x)\) associated with the outcomes \(x \in E\): 