Corollary 7.3 . [01BT] 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 structured objects have an unresolved mathematical role; their permanent tags identify source occurrences only. Complete original source context · Original author HTML
Corollary 7.3 .
Assume that ω \omega φ ∈ ℰ 1 ( X , ω ) \varphi\in\mathcal{E}^{1}(X,\omega) f ∈ C 0 ( X ) f\in C^{0}(X) P ω ( φ + t f ) ∈ ℰ 1 ( X , ω ) P_{\omega}(\varphi+tf)\in\mathcal{E}^{1}(X,\omega) t ∈ 𝐑 t\in\mathbf{R}
d d t | t = 0 E ω ∘ P ω ( φ + t f ) = ∫ f MA ( φ ) . \frac{d}{dt}\bigg|_{t=0}E_{\omega}\circ P_{\omega}(\varphi+tf)=\int f\,\MA(\varphi).