Proposition 4.4 . [00RG]

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 4.4.

In the chart $U^{s}_{w}$ the average function $\bar{\phi}$ is convex, and on the shrinked chart $U^{s}_{w,\delta}$ it has a Lipschitz bound:

|\bar{\phi}|\leq C,\quad|\bar{\phi}(x)-\bar{\phi}(x^{\prime})|\leq C|x-x^{\prime}|.

(23)