Lemma 2.3 . [007W]

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Lemma 2.3.

(Almost maximum on top strata) For $u\in PSH(X_{t},\omega_{t})$ normalised to $\sup_{X_{t}}u=0$ , there is some $i\in I$ , such that

\sup_{E_{i}^{0}}u\geq-C,\quad\int_{E_{i}^{0}}u\omega_{\mathcal{X}}|_{X_{t}}^{n}\geq-C^{\prime}.