On a theorem of Avanissian-Arsove (Q1123292)

The author proves that if \(\Omega\) is an open set in \({\mathbb{R}}^{p+q}\), where \(p\geq 2\) and \(q\geq 2\), v is separately subharmonic in \(\Omega\) and if for some positive r there exists a function \(u\in L^ r_{loc}(\Omega)\) such that \(v\leq u\) in \(\Omega\), then v is subharmonic in \(\Omega\).