Aufgaben:Problem 15

Let \( f \) be a continuous real-valued function on \( \mathbb{R}^n \). Let \(B = B_1(0) \) denote the unit ball in \( \mathbb{R}^3 \) . We define

$$ 1_B= \begin{cases} 1 \space x \in B \\ 0\space x\notin B \end{cases} $$

and a linear map

$$ f \cdot \mu_{\partial B} : \mathcal D (\mathbb{R}^3) \rightarrow \mathbb{R}^3 $$ $$ \phi \mapsto (f \cdot \mu_{\partial B})(\phi) = \int_{\partial B} $$