Asymptotics of $\delta $-subharmonic functions and their associated measures

The relationship of asymptotic behavior of the difference of two subharmonic functions $u_1-u_2$ in a neighborhood of infinity and of the difference of their associative measures $\mu_1-\mu_2$ is considered. The asymptotic behavior of difference is considered outside the exceptional sets of “power” smallness, namely, outside the set, which for any $\gamma$ admits covering by the circles $B(z_j,r_j)$, such that
$$ \sum_{R/2\le|z_j|\le R}r_j=o(R^{\gamma+1}),\qquad R\to\infty. $$
Asymptotics of the difference of associated measures is characterized by the behavior of the function
$$ \max_{R\le|z|/2}\biggl|\int_0^R\frac{\mu_1(z,t)-\mu_2(z,t)}t\,dt\biggr| $$
at infinity.