Bounded characteristic
= Bounded characteristic
A <holomorphic function> on the <unit disc> has bounded characteristic when $\sup_{r<1}\int\log^+|f(r\xi)|\,dm(\xi)<\infty$, where $\log^+t=\max(0,\log t)$. Thus it belongs to the <Nevanlinna class>. A general <meromorphic function> requires the additional pole-counting term in its characteristic; the displayed analytic definition has no such term.