Theorem. necessary and sufficient conditions for $\mathbb{f} \in \mathscr{C}'(E)$ [br921]
Theorem. necessary and sufficient conditions for $\mathbb{f} \in \mathscr{C}'(E)$ [br921]
Suppose $\mathbf{f}$ maps an open set $E \subset \mathbb{R}^{n}$ into $\mathbb{R}^{m}$. Then $\mathbf{f} \in \mathscr{C}'(E)$ if and only if the partial derivatives $D_{j}f_{i}$ exist and are continuous on $E$ for $1 \leq i \leq m, 1 \leq j \leq n$.