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In a recent preprint published on arXiv (see arXiv:2308.02993v2, referredhere as \cite{NXH}), N.X. Hong stated that every plurifinely open set $U\subset\mathbb{C}^n$, $n\geq 1$, is of the form $U=\bigcup \{\varphi_j>-1\}$, whereeach $\phi_j$ is a negative plurisubharmonic function defined on an open ball$B_j\subset \mathbb{C}^n$ and used this result to prove an equality result oncomplex Monge-Amp\`ere measures. Unfortunately, this result is wrong as we willsee below.

A note on the structure of plurifinely open sets and the equality of some complex Monge-Amp\`ere measures