PomeDefinition 8.11.2.FA49D2074193 For Borel $E\subset U$ define the smooth capacity
\[ c_ s(E)=\sup \left\{ \int _ E \Lambda _ s(a): a\in C^\infty (U),\ -1\leq a\leq 0, \mathrm{dd}^{\mathrm{c}}a\in \overline{\Gamma _ m(\omega )}\right\} , \]
for $0\leq s\leq m$. Its outer-open version is
\[ c_ s^*(E)=\inf \{ c_ s(G):E\subset G\subset U,\ G\text{ open}\} . \]
A function on a compact $K\Subset U$ is quasicontinuous for this capacity if, for every $\epsilon >0$, it is continuous on $K\setminus G$ for some open $G\subset U$ with $c_ s(G)<\epsilon $.
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