I came across the following exercise on plurisubharmonic functions (Krantz, function theory of several complex variables, §111):
Let $\Omega \subseteq \mathbb{C}^n$ be a domain, $f: \Omega \to \mathbb{R}$ continuous. Suppose that for each compact $K \subset \subset \Omega$ and for each $h \in C(K)$ that is pluriharmonic function on $ \mathring { K } $, it holds that $h\ge f$ on $ \partial K$ implies $h \ge f$ on $K$. Then $f$ is plurisubharmonic.
Is it true or false? Any help or insight is deeply appreciated.