Lemma 3.2 . [02DT]

Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.

Complete original source context · Original author HTML

Lemma 3.2.

Let $V$ be a $n$ -dimensional compact normal Kähler space and $\Omega$ be a smooth Kähler form on $V$ . Let $\pi:X\to V$ a resolution, $\omega=\pi^{*}\Omega$ , and let $d\lambda$ be a positive definite smooth volume form on $X$ .

If $\mu=f_{1}d\lambda$ , with $f_{1}\in L^{p}(X,d\lambda)$ for some $p>1$ , then there exists $p^{\prime}>1$ such that $\mu=f\omega^{n}$ and $f\in L^{p^{\prime}}(X,\omega^{n})$ .