Proposition 4.24 . [053A] 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 Source fidelity gap: the original arXiv HTML omits an author TeX footnote attached to equation e:def-omega, including its reference to Remark r:error-function. The retained HTML is preserved as published; the original author TeX remains available. TeX correspondence is not complete. Complete original source context · Original author HTML
Proposition 4.24 .
For T T ( ω T ′ , Ω T ′ ) (\omega_{T}^{\prime},\Omega_{T}^{\prime}) C 1 , α C^{1,\alpha} 𝒱 \mathcal{V} α ∈ ( 0 , 1 ) \alpha\in(0,1) δ , μ , ν ∈ ℝ \delta,\mu,\nu\in\mathbb{R}
(4.323) | Ω T ′ − Ω T | C δ , μ , ν 2 , α ( 𝒱 ) \displaystyle|\Omega_{T}^{\prime}-\Omega_{T}|_{C^{2,\alpha}_{\delta,\mu,\nu}(\mathcal{V})} = ϵ ¯ T 2 , \displaystyle=\underline{\epsilon}_{T^{2}},
(4.324) | ω T ′ − ω T | C δ , μ , ν 1 , α ( 𝒱 ) \displaystyle|\omega_{T}^{\prime}-\omega_{T}|_{C^{1,\alpha}_{\delta,\mu,\nu}(\mathcal{V})} = ϵ ¯ T 2 . \displaystyle=\underline{\epsilon}_{T^{2}}.