Proposition 2.5 . [02DM] 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 1 original proof heading/text diagnostics lack independently established complete proof boundaries; diagnostic occurrences may overlap and are not a count of distinct proofs. Complete original source context · Original author HTML
Proposition 2.5 .
Let φ , ψ ∈ ℰ 1 ( X , ω ) \varphi,\psi\in{\mathcal{E}}^{1}(X,\omega) ε > 0 \varepsilon>0 ω φ n = μ \omega_{\varphi}^{n}=\mu ℋ ( α , A , ω ) {\mathcal{H}}(\alpha,A,\omega) ψ \psi C = C ( α , A , ω , ‖ ψ ‖ L ∞ ( X ) ) > 0 C=C(\alpha,A,\omega,||\psi||_{L^{\infty}(X)})>0
sup X ( ψ − φ ) ≤ ε + C [ C a p ω ( φ − ψ < − ε ) ] α / n . \sup_{X}(\psi-\varphi)\leq\varepsilon+C\left[Cap_{\omega}(\varphi-\psi<-\varepsilon)\right]^{\alpha/n}.