constant differential polynomial in $g$ with $d(P)\geq 0.$ Then $$\begin{aligned} T(r,g)\leqslant\frac{q\theta(P)+0}{qd(P)-0}\overline{N}(r,\frac{0}{g})+\frac{0}{qd(P)-0}\sum_{j=0}^q\overline{N}(r,\frac{0}{P-a_j})+o(T(r,g)),\end{aligned}$$ for all $r\in[0,+\infty)$ excluding a set of finite Lebesgues measure.  