TeX source:

\rho = \sum_m\Pr\{m\}\rho_m = \sum_m\text{tr}(\mathbf{M}_m^\dagger\mathbf{M}_m\rho)\dfrac{\mathbf{M}_m\rho\mathbf{M}_m^\dagger}{\text{tr}(\mathbf{M}_m^\dagger\mathbf{M}_m\rho)} = \sum_m\mathbf{M}_m\rho\mathbf{M}_m^\dagger,