Proposition 19.8.2F2503E6C53F2

Proposition 19.8.2.F2503E6C53F2 Let $v\in \mathrm{QPSH}(X)$, let $D,E\geq 0$, and let $F\in C^\infty (X,\mathbb R)$. Suppose that $|u-v|\leq D$ outside the union of the pole sets of $u$ and $v$, and that $\mathrm{d}V'=\mathrm{e}^ F \mathrm{d}V$ with $|F|\leq E$. Then $u$ and $v$ have the same section spaces, and for every positive integer $m$ and every $s$ in the common space $\mathcal H_ m(u)=\mathcal H_ m(v)$,