Un'osservazione sulla differenziabilità (Q1138104)

Theorem. Let \(E\) be an open set in \(\mathbb R^n\), \(f: E\to\mathbb R\) and \(F_n\) the interval function associated to \(f\). If \(f\) is differentiable a.e. for all groupages of \((n-1)\)-variables, and \(0<\alpha<1\), the following conditions are equivalent: 1. \(f\) is differentiable a.e. in \(E\). 2. \(F_n\) is \(\alpha\)-Lipschitzian a.e. in \(E\). 3. \(F_n\) is almost \(\alpha\)-absolutely continuous in \(E\). 4. \(F_n\) is of almost \(\alpha\)-bounded variation in \(E\).