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Lemma 18.28.42E97173FEFAFD

Lemma 18.28.42.E97173FEFAFD Let $v_1,v_2\colon K\rightarrow [-\infty ,\infty )$ be two measurable functions such that

  1. 7AB5A208122C

    $v_1\leq v_2$;

  2. 60A51A0A77E1

    $\{ v_1=-\infty \} =\{ v_2=-\infty \} $.

Then for any $s\in \mathrm{H}^0(X,L^ k\otimes T)$ ($k\geq 1$), we have

\[ N_{v_1,K}^ k(s)\geq N_{v_2,K}^ k(s). \]

Proof. This follows immediately from the definition (18.28.40). $\square$

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