\int\left\Vert \phi(z,\hat{\gamma}_{\ell},\hat{\lambda}_{\ell})-\phi (z,\gamma_{0},\hat{\lambda}_{\ell})-\phi(z,\hat{\gamma}_{\ell},\lambda _{0})+\phi(z,\gamma_{0},\lambda_{0})\right\Vert ^{0}F_{0}(dz)\overset{p}{\longrightarrow}0