Corollary 4.8 . [00RN]

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Corollary 4.8.

(Local $L^{1}$ -oscillation bound) Over one log scale inside $U_{w,\delta}^{s}$ ,

\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_{|z^{m_{i}}|\sim|z^{m_{i}}(P)|}|\phi-\bar{\phi}|d\mu_{s}\leq Cs^{-1/2}.