PomeDefinition 16.25.5.E9BD67F94210 For a reference potential $\phi \in \mathrm{PSH}(X,\theta )$ and a Borel set $A\subset X$, the Monge–Ampère capacity relative to $\phi $ is
\[ \operatorname {Cap}_{\theta ,\phi }(A) =\sup \{ \mu _ v(A):v\in \mathrm{PSH}(X,\theta ),\ \phi -1\leq v\leq \phi \} . \]
The potentials $v$ in this supremum are called competitors for $\operatorname {Cap}_{\theta ,\phi }$. For $\phi =V_\theta $ we obtain the $\theta $-capacity.
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