Example 5.15.328F2383E9245

Example 5.15.3.28F2383E9245 Let $\varphi \in \mathrm{PSH}(\Omega )$ and $C\in \mathbb {R}$. Then the sets $\{ \varphi >C\} $ and $\{ \varphi <C\} $ are both $\mathcal{F}$-open.

In fact, the latter case follows from proposition 5.15.2, while the former follows from the observation