ScalingStacks

Proposition 2.6 . [0330]

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Proposition 2.6.

If PP is a P​S​H​(X,ω)PSH(X,\omega)-polar set, then C​a​pω​(P)=0Cap_{\omega}(P)=0. More precisely, if ψ∈P​S​H−​(X,ω)\psi\in PSH^{-}(X,\omega) then

C​a​pω​(ψ<−t)≤1t​[∫X(−ψ)​ωn+n​V​o​lω​(X)],∀t>0.Cap_{\omega}(\psi<-t)\leq\frac{1}{t}\left[\int_{X}(-\psi)\omega^{n}+nVol_{\omega}(X)\right],\;\forall t>0.

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