Proposition 6.11 . [01BK] Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.
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Proposition 6.11 .
For any φ , ψ ∈ ℰ 1 ( X , ω ) \varphi,\psi\in\mathcal{E}^{1}(X,\omega)
(6.6) 𝟏 { φ > ψ } MA ( max { φ , ψ } ) = 𝟏 { φ > ψ } MA ( φ ) , \one_{\{\varphi>\psi\}}\MA(\max\{\varphi,\psi\})=\one_{\{\varphi>\psi\}}\MA(\varphi),
and the comparison principle holds:
(6.7) ∫ { φ < ψ } MA ( ψ ) ≤ ∫ { φ < ψ } MA ( φ ) . \int_{\{\varphi<\psi\}}\MA(\psi)\leq\int_{\{\varphi<\psi\}}\MA(\varphi).