 More generally, if \(\mu_i, i=1,2,\ldots\), are probability measures on \(L(\mathbf{H})\), then so is any “mixture”, or convex combination \(\mu = \sum_i t_i\mu_i\) where \(0\le t_i\le 1\) and \(\sum_i t_i = 1\). Given any sequence \(u_1, u_2,\ldots\), of unit vectors, let \(\mu_i = \mu_{u_{ i}}\) and let \(P_i = P_{u_{ i}}\). Forming the operator 