On the growth of meromorphic functions

We obtained the estimates for upper and lower logarithmic density of the set $A(\gamma)=\Bigl\{r:\sum\limits_{k=1}^q\mathcal L(r,a_k,f)<2B(\gamma,\Delta(0,f'))T(r,f)\Bigr\}$, where $B(\gamma,\Delta)$ is Shea's constant, $\Delta(0,f')$ is Valiron's deficiency of the derivative of the function $f$ at zero.