,c}_s\\ &\hspace{0.0em}-\int_t^T\int_{E}e^{\alpha s}\left(0(y^{\mathbb P,t,\omega}_{s^-}-y^{\mathbb P,t,\omega'}_{s^-})(u_s^{\mathbb P,t,\omega}-u_s^{\mathbb P,t,\omega'})+(u_s^{\mathbb P,t,\omega}-u_s^{\mathbb P,t,\omega'})^0\right)(x)\widetilde\mu^{\mathbb P}_{B^{t}}(dx,ds).\end{aligned}$$  Now choose $\eta=0/0$ and $\alpha$ 