Lemma 6.8 . [01BD]

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Lemma 6.8.

If $0\geq\varphi\in\mathcal{E}^{1}(X,\omega)$ and $f\in\mathcal{D}(X)$ , then

\left|\int f\MA(\varphi^{\langle t\rangle})-\int f\MA(\varphi)\right|\leq\frac{2(n+1)}{t}|E_{\omega}(\varphi)|\sup_{X}|f|

for any $t>0$ .