L’espace linéaire des fonctions cliquées sur est généré par les fonctions quasi-continues
Lineare zweidimensionale Räume von stetigen Funktionen mit stetigen ersten Ableitungen
Lipschitz functions with unexpectedly large sets of nondifferentiability points.
Lipschitz r-continuity of the approximative subdifferential of a convex function.
Lusin-type Theorems for Cheeger Derivatives on Metric Measure Spaces
A theorem of Lusin states that every Borel function onRis equal almost everywhere to the derivative of a continuous function. This result was later generalized to Rn in works of Alberti and Moonens-Pfeffer. In this note, we prove direct analogs of these results on a large class of metric measure spaces, those with doubling measures and Poincaré inequalities, which admit a form of differentiation by a famous theorem of Cheeger.