Family of Subharmonic Functions and Separately Subharmonic Functions

Continuity of Subharmonic Functions

“…A set E is said to be thin at a point ζ if ζ is not a fine (with respect to the fine topology) limit point of E. The following theorem, used in the proof of Lemma 3.1,gives Proof. We closely follow the proof of Lemma 3.2. in author's paper [3]. The set E is open, since v is upper semi-continuous.…”