Proposition 4.1 . [00RB]

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Proposition 4.1.

(Harnack type inequality) Suppose $\varphi\in PSH(X_{s},s^{-1}\omega_{FS})$ with $\sup_{X_{s}}\varphi=0$ . Then the average integral

\mathchoice{{\vbox{\hbox{$\textstyle-$ }}\kern-7.83337pt}}{{\vbox{\hbox{$\scriptstyle-$ }}\kern-6.11674pt}}{{\vbox{\hbox{$\scriptscriptstyle-$ }}\kern-5.48965pt}}{{\vbox{\hbox{$\scriptscriptstyle-$ }}\kern-5.31259pt}}\!\int_{X^{toric}_{s}}|\varphi|d\mu_{s}\leq C.