Proposition 5.10 . [02T1] 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 5.10 .
The affine map A : N 1 , ℝ → N 2 , ℝ A\colon N_{1,\mathbb{R}}\to N_{2,\mathbb{R}} X Σ 1 ( ℝ ≥ 0 ) → X Σ 2 ( ℝ ≥ 0 ) X_{\Sigma_{1}}(\mathbb{R}_{\geq 0})\to X_{\Sigma_{2}}(\mathbb{R}_{\geq 0}) φ p , H \varphi_{p,H}
X Σ 1 an \textstyle{X_{\Sigma_{1}}^{{\text{\rm an}}}\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces} φ p , H \scriptstyle{\varphi_{p,H}} ρ Σ 1 \scriptstyle{\rho_{\Sigma_{1}}} X Σ 2 an \textstyle{X_{\Sigma_{2}}^{{\text{\rm an}}}\ignorespaces\ignorespaces\ignorespaces\ignorespaces} ρ Σ 2 \scriptstyle{\rho_{\Sigma_{2}}} X Σ 1 ( ℝ ≥ 0 ) \textstyle{X_{\Sigma_{1}}(\mathbb{R}_{\geq 0})\ignorespaces\ignorespaces\ignorespaces\ignorespaces} φ p , H \scriptstyle{\varphi_{p,H}} X Σ 2 ( ℝ ≥ 0 ) , \textstyle{X_{\Sigma_{2}}(\mathbb{R}_{\geq 0}),} X Σ 1 an \textstyle{X_{\Sigma_{1}}^{{\text{\rm an}}}\ignorespaces\ignorespaces\ignorespaces\ignorespaces} φ p , H \scriptstyle{\varphi_{p,H}} X Σ 2 an \textstyle{X_{\Sigma_{2}}^{{\text{\rm an}}}} X Σ 1 ( ℝ ≥ 0 ) \textstyle{X_{\Sigma_{1}}(\mathbb{R}_{\geq 0})\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces} φ p , H \scriptstyle{\varphi_{p,H}} θ Σ 1 \scriptstyle{\theta_{\Sigma_{1}}} X Σ 2 ( ℝ ≥ 0 ) . \textstyle{X_{\Sigma_{2}}(\mathbb{R}_{\geq 0}).\ignorespaces\ignorespaces\ignorespaces\ignorespaces} θ Σ 2 \scriptstyle{\theta_{\Sigma_{2}}}