(Stability estimate) Let $(X,\omega)$ be a compact Kähler manifold, and $\phi,\psi\in PSH(X,\omega)\cap C^{0}$, such that $\omega_{\phi}^{n}$ is absolutely continuous. Assume $\left\lVert\psi\right\rVert_{C^{0}}\leq A^{\prime}$ and the Skoda type estimate (2). Then there is a number $B(n,A,A^{\prime},\alpha)$, such that if $\frac{\int_{\phi-\psi\leq-t_{0}}\omega_{\phi}^{n}}{Vol(X)}<(2B)^{-2n}$ for some $t_{0}$, then

$$\min(\phi-\psi)\geq-t_{0}-4B\left(\frac{\int_{\phi-\psi\leq-t_{0}}\omega_{\phi}^{n}}{Vol(X)}\right)^{1/2n}.$$

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