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Notation: $U \subset R^n$, bounded open set $D^k(U) = \{ \omega : U \to \Lambda^k R^n : \text{compactly supported and infinitely differentiable \}}$ $D_k(U) = D^k(U)'$ is the topological dual space (...

Let $\mathcal{P}_{n:+}(\mathbb{R})$ denote the set of probability measures on $\mathbb{R}$ for the form $\sum_{i=1}^n k_i \delta_{x_i}$ where $k_i>0$. Then any measure in $\mathcal{P}_{n:+}(\...