Theorem 8.1 . [01DD]

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

Theorem 8.1.

For any $\phi\in{\mathcal{E}}^{1}({L^{\mathrm{an}}})$ and $f\in C^{0}({X^{\mathrm{an}}})$ , the function $t\mapsto E(P(\phi+tf))$ is differentiable at $t=0$ , with derivative $\frac{d}{dt}E(\phi+tf)|_{t=0}=\int f\operatorname{MA}(\phi)$ .