  Let $\varphi$ be a quasi-psh function on a complex manifold $X$ and let
$S\subset X$ be a complex submanifold. Then the multiplier ideal sheaves
$\mathcal{I}(\varphi|_S)\subset\mathcal{I}(\varphi)|_{S}$ and the complex
singularity exponents $c_{x}\left(\varphi|_{S}\right)\leqslant c_{x}(\varphi)$
by Ohsawa-Takegoshi $L^{2}$ extension theorem. An interesting question is to
know whether it is possible to get equalities in the above formulas. In the
present article, we show that the answer is positive when $S$ is chosen outside
a measure zero set in a suitable projective space.
