ScalingStacks

Lemma 2.2 . [02DH]

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Lemma 2.2.

Let φ,ψ∈ℰ1​(X,ω)\varphi,\psi\in{\mathcal{E}}^{1}(X,\omega) be two negative functions. Then for all s>0s>0 and 0≤t≤10\leq t\leq 1,

tn​C​a​pω​(φ−ψ<−s−t)≤∫(φ−ψ<−s−t​ψ)ωφn.t^{n}Cap_{\omega}(\varphi-\psi<-s-t)\leq\int_{(\varphi-\psi<-s-t\psi)}\omega_{\varphi}^{n}.

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