Abstract

Let M be the set of all functions meromorphic on D={z∈ℂ:|z|<1}. For a∈(0,1], a function f∈M is called a-normal function of bounded (vanishing) type or f∈Na(N0a), if supz∈D(1−|z|)af#(z)<∞ (lim|z|→1(1−|z|)af#(z)=0). In this paper we not only show the discontinuity of Na and N0a relative to containment as a varies, which shows ∪0<a<1Na⊂UBC0, but also give several characterizations of Na and N0a which are real extensions for characterizations of N and N0.