PomeExample 20.2.3.DC6BE2600DA0 Consider a psh function $\varphi $ in two variables, say
\[ \varphi (z,w)=\left( -\log (-\log |z|^2)\right) \lor \left(\log |w|^2\right). \]
Take an arbitrary quasi-equisingular approximation $(\varphi _ j)_ j$. Then each $\varphi _ j$ is locally bounded since $\nu (\varphi ,(0,0))=0$. Let us consider the restrictions to $H=\{ z=0\} $. Then $\varphi _ j|_ H$ is still bounded, while
\[ \varphi |_ H(w)=\log |w|^2. \]
In other words, the restrictions $\varphi _ j|_ H$ fail to be a quasi-equisingular approximation of $\varphi |_ H$.
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