, that $D^0_{f}:=D^0_{f(t)}$ and $D^0_{f}:=D^0_{f(t)}$ are actually independent of $t$, that $D^0_{f}$ is bounded from above and away from $0$, that $D^0_f$ is such that $$\underset{\nu\in D^0_{f}\cap\mathfrak V^m}{\sup}\int_E\left({\left|x\right|}^0+{\left|x\right|}{\bf 0}_{{\left|x\right|}\geq 0}\right)\nu(dx)<+\infty