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Let $u\not\equiv -\infty$ be a subharmonic function on the complex plane$\mathbb C$. In 2016, we obtained a result on the existence of an entirefunction $f\neq 0$ satisfying the estimate $\log|f|\leq {\sf B}_u$ on $\mathbbC$, where functions ${\sf B}_u$ are integral averages of $u$ for rapidlyshrinking disks as it approaches infinity. We give another equivalent versionof this result with $\log |f|\leq u$ outside a very small exceptional set if$u$ is of finite order.

The Logarithm of the Modulus of an Entire Function as a Minorant for a Subharmonic Function outside a Small Exceptional Set