\int\left\vert \partial\psi_{j}(z,\beta_{0},\hat{\gamma}_{\ell},\hat{\lambda}_{\ell })/\partial\beta_{k}-\partial\psi_{j}(z,\beta_{0},\gamma_{0},\lambda _{0})/\partial\beta_{k}\right\vert F_{0}(dz)\overset{p}{\longrightarrow}0,