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
$$\limsup_{r\to\infty}\log|f(re^{it})|\leq \limsup_{|z|\to\infty}\log|f(z)|$$