Proposition 5.9 . [02T0] Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.
Complete original source context · Original author HTML
Proposition 5.9 .
The natural map N ( σ ) ℝ ↪ N σ N(\sigma)_{\mathbb{R}}\hookrightarrow N_{\sigma} X Σ ( σ ) ( ℝ ≥ 0 ) → X Σ ( ℝ ≥ 0 ) X_{\Sigma(\sigma)}(\mathbb{R}_{\geq 0})\to X_{\Sigma}(\mathbb{R}_{\geq 0})
X Σ ( σ ) an \textstyle{X_{\Sigma(\sigma)}^{{\text{\rm an}}}\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces} ρ Σ ( σ ) \scriptstyle{\rho_{\Sigma(\sigma)}} X Σ an \textstyle{X_{\Sigma}^{{\text{\rm an}}}\ignorespaces\ignorespaces\ignorespaces\ignorespaces} ρ Σ \scriptstyle{\rho_{\Sigma}} X Σ ( σ ) ( ℝ ≥ 0 ) \textstyle{X_{\Sigma(\sigma)}(\mathbb{R}_{\geq 0})\ignorespaces\ignorespaces\ignorespaces\ignorespaces} X Σ ( ℝ ≥ 0 ) , \textstyle{X_{\Sigma}(\mathbb{R}_{\geq 0}),} X Σ ( σ ) an \textstyle{X_{\Sigma(\sigma)}^{{\text{\rm an}}}\ignorespaces\ignorespaces\ignorespaces\ignorespaces} X Σ an \textstyle{X_{\Sigma}^{{\text{\rm an}}}} X Σ ( σ ) ( ℝ ≥ 0 ) \textstyle{X_{\Sigma(\sigma)}(\mathbb{R}_{\geq 0})\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces} θ Σ ( σ ) \scriptstyle{\theta_{\Sigma(\sigma)}} X Σ ( ℝ ≥ 0 ) . \textstyle{X_{\Sigma}(\mathbb{R}_{\geq 0}).\ignorespaces\ignorespaces\ignorespaces\ignorespaces} θ Σ \scriptstyle{\theta_{\Sigma}}