. Let $X$ be a compact complex manifold, let $\Omega>0$ be a smooth volume form and let $\sigma_{j}\in H^{0}(X,E_{j})$, $\tau_{r}\in H^{0}(X,F_{r})$, $j=1,...,N$, $r=1,...,M$ be, non identically zero, holomorphic sections of some holomorphic vector bundles over $X$ such that the integral condition

$\displaystyle\int\limits_{X}\,\prod\limits_{j=1}^{N}|\sigma_{j}|^{2l_{j}}\cdot\prod\limits_{r=1}^{M}|\tau_{r}|^{-2h_{r}}\,\Omega<+\infty$

holds for some real numbers $l_{j}\geq 0,\,h_{r}\geq 0$. Then the integrand function belongs to some $L^{p}$ space, $p>1$ and the family of functions

$\displaystyle G_{\varepsilon}:=\prod\limits_{j=1}^{N}(|\sigma_{j}|^{2}+\varepsilon^{A})^{l_{j}}\cdot\prod\limits_{r=1}^{M}(|\tau_{r}|^{2}+\varepsilon)^{-h_{r}}\,,$

$\varepsilon\in[0,1)$, $A:=(\sum_{r}h_{r}+1)/(\min_{j}l_{j})$, converges in $L^{p}$-norm to function $G_{0}$ when $\varepsilon\rightarrow 0$.