What is the relation between $\limsup_{r\to\infty}\log|f(re^{it})|$ and $\limsup_{|z|\to\infty}\log|f(z)|$ where $z=re^{it}$, $r>0, 0
I know that the first one is a function of $t$, but the second one is a constant (assuming both limits exist), I'm told that I have this relation but I don't know why?? any help
$\limsup_{r\to\infty}\log|f(re^{it})|\leq \limsup_{|z|\to\infty}\log|f(z)|$