Let $f$ be an holomrphic function in $\mathbb C$. Is the functions $\sup_{|z| = r} |f(z)|$ continuous as a function of $r$?
I think that yes but I'm not sure.
(I edited the question, adding the modulus for the function)
Let $f$ be an holomrphic function in $\mathbb C$. Is the functions $\sup_{|z| = r} |f(z)|$ continuous as a function of $r$?
I think that yes but I'm not sure.
(I edited the question, adding the modulus for the function)