Definition 2.8 . [0389] Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.
Source coverage notes 9 original structured objects have an unresolved mathematical role; their permanent tags identify source occurrences only. Complete original source context · Original author HTML
Definition 2.8 .
Let X X K K θ ∈ 𝒵 1 , 1 ( X ) \theta\in\mathcal{Z}^{1,1}(X) { θ } ∈ N 1 ( X ) \{\theta\}\in N^{1}(X) θ \theta u ∈ C 0 ( X ) u\in C^{0}(X)
(2.2) P θ ( u ) : X → ℝ , P θ ( u ) ( x ) = sup { φ ( x ) | φ ∈ PSH 𝒟 ( X , θ ) ∧ φ ≤ u } . {P}_{\theta}(u)\colon X\to\mathbb{R},\,\,{P}_{\theta}(u)(x)=\sup\{\varphi(x)\,|\,\varphi\in{\rm PSH}_{\mathscr{D}}(X,\theta)\wedge\varphi\leq u\}.